diff --git a/CHANGELOG.md b/CHANGELOG.md
index 415553996..2df1ae195 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,11 +12,17 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Add a multibody friction cone cost ([#234](https://github.com/Simple-Robotics/aligator/pull/234))
 - Add a `GravityCompensationResidual`, modelling $r(x,u) = Bu - G(q)$ ([#235](https://github.com/Simple-Robotics/aligator/pull/235))
 - Add Pixi support ([#240](https://github.com/Simple-Robotics/aligator/pull/240))
+- Added a nonmonotone linesearch procedure ([#244](https://github.com/Simple-Robotics/aligator/pull/244))
+- Add enum value `StepAcceptanceStrategy::LINESEARCH_NONMONOTONE` ([#244](https://github.com/Simple-Robotics/aligator/pull/244))
 
 ### Changed
 
+- **API BREAKING:** Change enum value `StepAcceptanceStrategy::LINESEARCH` to `LINESEARCH_NONMONOTONE` ([#244](https://github.com/Simple-Robotics/aligator/pull/244))
+  - Add constructor argument `StepAcceptanceStrategy sa_strategy`, defaults to nonmonotone
+- The minimum required version of proxsuite-nlp is now 0.10.0 ([#244](https://github.com/Simple-Robotics/aligator/pull/244))
 - `SolverProxDDP`: add temporary vectors for linesearch
 - `SolverProxDDP`: remove exceptions from `computeMultipliers()`, return a bool flag
+- HistoryCallback: take solver instance as argument
 - `gar`: rework and move sparse matrix utilities to `gar/utils.hpp`
 - `SolverProxDDP`: Rename `maxRefinementSteps_` and `refinementThreshold_` to snake-case
 - `SolverProxDDP`: make `linesearch_` public
diff --git a/CMakeLists.txt b/CMakeLists.txt
index dce8ac665..accbc6d39 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -216,7 +216,7 @@ set(BOOST_REQUIRED_COMPONENTS filesystem)
 set_boost_default_options()
 export_boost_default_options()
 add_project_dependency(Boost REQUIRED COMPONENTS ${BOOST_REQUIRED_COMPONENTS})
-add_project_dependency(proxsuite-nlp 0.8.0 REQUIRED PKG_CONFIG_REQUIRES "proxsuite-nlp >= 0.8.0")
+add_project_dependency(proxsuite-nlp 0.10.0 REQUIRED PKG_CONFIG_REQUIRES "proxsuite-nlp >= 0.10.0")
 
 if(BUILD_WITH_PINOCCHIO_SUPPORT)
   message(STATUS "Building aligator with Pinocchio support.")
diff --git a/bindings/python/aligator/utils/plotting.py b/bindings/python/aligator/utils/plotting.py
index f29a02b76..4b2dc4891 100644
--- a/bindings/python/aligator/utils/plotting.py
+++ b/bindings/python/aligator/utils/plotting.py
@@ -4,7 +4,14 @@
 from aligator import HistoryCallback, Results
 
 
-def plot_convergence(cb: HistoryCallback, ax: plt.Axes, res: Results = None):
+def plot_convergence(
+    cb: HistoryCallback,
+    ax: plt.Axes,
+    res: Results = None,
+    *,
+    show_al_iters=False,
+    legend_kwargs={},
+):
     from proxsuite_nlp.utils import plot_pd_errs
 
     prim_infeas = cb.prim_infeas.tolist()
@@ -14,7 +21,28 @@ def plot_convergence(cb: HistoryCallback, ax: plt.Axes, res: Results = None):
         dual_infeas.append(res.dual_infeas)
     plot_pd_errs(ax, prim_infeas, dual_infeas)
     ax.grid(axis="y", which="major")
-    return
+    handles, labels = ax.get_legend_handles_labels()
+    labels += [
+        "Prim. err $p$",
+        "Dual err $d$",
+    ]
+    if show_al_iters:
+        prim_tols = np.array(cb.prim_tols)
+        al_iters = np.array(cb.al_index)
+        labels.append("$\\eta_k$")
+
+        itrange = np.arange(len(al_iters))
+        if itrange.size > 0:
+            if al_iters.max() > 0:
+                labels.append("AL iters")
+            ax.step(itrange, prim_tols, c="green", alpha=0.9, lw=1.1)
+            al_change = al_iters[1:] - al_iters[:-1]
+            al_change_idx = itrange[:-1][al_change > 0]
+
+            ax.vlines(al_change_idx, *ax.get_ylim(), colors="gray", lw=4.0, alpha=0.5)
+
+    ax.legend(labels=labels, **legend_kwargs)
+    return labels
 
 
 def plot_se2_pose(
@@ -50,6 +78,7 @@ def plot_controls_traj(
     joint_names=None,
     rmodel=None,
     figsize=(6.4, 6.4),
+    xlabel="Time (s)",
 ) -> tuple[plt.Figure, list[plt.Axes]]:
     t0 = times[0]
     tf = times[-1]
@@ -57,7 +86,9 @@ def plot_controls_traj(
     nu = us.shape[1]
     nrows, r = divmod(nu, ncols)
     nrows += int(r > 0)
-    if axes is None:
+
+    make_new_plot = axes is None
+    if make_new_plot:
         fig, axes = plt.subplots(nrows, ncols, sharex="col", figsize=figsize)
     else:
         fig = axes.flat[0].get_figure()
@@ -77,9 +108,13 @@ def plot_controls_traj(
             ax.set_ylim(*ylim)
         if joint_names is not None:
             joint_name = joint_names[i].lower()
-            ax.set_ylabel(joint_name)
-    fig.supxlabel("Time $t$")
-    fig.suptitle("Control trajectories")
+            ax.set_title(joint_name, fontsize=8)
+    if nu > 1:
+        fig.supxlabel(xlabel)
+        fig.suptitle("Control trajectories")
+    else:
+        axes[0].set_xlabel(xlabel)
+        axes[0].set_title("Control trajectories")
     fig.tight_layout()
     return fig, axes
 
@@ -92,6 +127,7 @@ def plot_velocity_traj(
     ncols=2,
     vel_limit=None,
     figsize=(6.4, 6.4),
+    xlabel="Time (s)",
 ) -> tuple[plt.Figure, list[plt.Axes]]:
     vs = np.asarray(vs)
     nv = rmodel.nv
@@ -111,7 +147,7 @@ def plot_velocity_traj(
     tf = times[-1]
 
     if axes is None:
-        fig, axes = plt.subplots(nrows, ncols, figsize=figsize)
+        fig, axes = plt.subplots(nrows, ncols, sharex=True, figsize=figsize)
         fig: plt.Figure
     else:
         fig = axes.flat[0].get_figure()
@@ -127,9 +163,9 @@ def plot_velocity_traj(
             ax.hlines(-vel_limit[i], t0, tf, colors="k", linestyles="--")
             ax.hlines(+vel_limit[i], t0, tf, colors="r", linestyles="dashdot")
             ax.set_ylim(*ylim)
-        ax.set_ylabel(joint_name)
+        ax.set_title(joint_name, fontsize=8)
 
-    fig.supxlabel("Time $t$")
+    fig.supxlabel(xlabel)
     fig.suptitle("Velocity trajectories")
     fig.tight_layout()
     return fig, axes
diff --git a/bindings/python/src/expose-callbacks.cpp b/bindings/python/src/expose-callbacks.cpp
index 49016bfbf..d65561b6e 100644
--- a/bindings/python/src/expose-callbacks.cpp
+++ b/bindings/python/src/expose-callbacks.cpp
@@ -2,21 +2,29 @@
 #include "aligator/python/callbacks.hpp"
 #include "aligator/helpers/history-callback.hpp"
 
+#include "aligator/solvers/proxddp/solver-proxddp.hpp"
+#include "aligator/solvers/fddp/solver-fddp.hpp"
+
 namespace aligator {
 namespace python {
 
 using context::Scalar;
+using context::SolverFDDP;
+using context::SolverProxDDP;
+using HistoryCallback = HistoryCallbackTpl<Scalar>;
+
+#define ctor(Solver)                                                           \
+  bp::init<Solver *, bool, bool>(                                              \
+      ("self"_a, "solver", "store_pd_vars"_a = true, "store_values"_a = true))
 
 void exposeHistoryCallback() {
-  using HistoryCallback = HistoryCallbackTpl<Scalar>;
 
   bp::scope in_history =
       bp::class_<HistoryCallback, bp::bases<CallbackBase>>(
           "HistoryCallback", "Store the history of solver's variables.",
-          bp::init<bool, bool, bool>((bp::arg("self"),
-                                      bp::arg("store_pd_vars") = true,
-                                      bp::arg("store_values") = true,
-                                      bp::arg("store_residuals") = true)))
+          bp::no_init)
+          .def(ctor(SolverProxDDP))
+          .def(ctor(SolverFDDP))
 #define _c(name) def_readonly(#name, &HistoryCallback::name)
           ._c(xs)
           ._c(us)
@@ -36,9 +44,8 @@ void exposeHistoryCallback() {
 void exposeCallbacks() {
   bp::register_ptr_to_python<shared_ptr<CallbackBase>>();
 
-  bp::class_<CallbackWrapper, boost::noncopyable>("BaseCallback",
-                                                  "Base callback for solvers.",
-                                                  bp::init<>(bp::args("self")))
+  bp::class_<CallbackWrapper, boost::noncopyable>(
+      "BaseCallback", "Base callback for solvers.", bp::init<>(("self"_a)))
       .def("call", bp::pure_virtual(&CallbackWrapper::call),
            bp::args("self", "workspace", "results"));
 
diff --git a/bindings/python/src/expose-solver-prox.cpp b/bindings/python/src/expose-solver-prox.cpp
index 750892589..d05c9dfd4 100644
--- a/bindings/python/src/expose-solver-prox.cpp
+++ b/bindings/python/src/expose-solver-prox.cpp
@@ -7,6 +7,7 @@
 #include "aligator/solvers/proxddp/solver-proxddp.hpp"
 
 #include <eigenpy/std-unique-ptr.hpp>
+#include <eigenpy/variant.hpp>
 
 namespace aligator {
 namespace python {
@@ -19,8 +20,8 @@ void exposeProxDDP() {
   using context::VectorRef;
   using context::Workspace;
 
-  eigenpy::register_symbolic_link_to_registered_type<
-      Linesearch<Scalar>::Options>();
+  using LsOptions = Linesearch<Scalar>::Options;
+  eigenpy::register_symbolic_link_to_registered_type<LsOptions>();
   eigenpy::register_symbolic_link_to_registered_type<LinesearchStrategy>();
   eigenpy::register_symbolic_link_to_registered_type<
       proxsuite::nlp::LSInterpolation>();
@@ -74,6 +75,7 @@ void exposeProxDDP() {
       .def(PrintableVisitor<Results>());
 
   using SolverType = SolverProxDDPTpl<Scalar>;
+  using ls_variant_t = SolverType::LinesearchVariant::variant_t;
 
   auto cls =
       bp::class_<SolverType, boost::noncopyable>(
@@ -84,9 +86,10 @@ void exposeProxDDP() {
           " The solver instance initializes both a Workspace and a Results "
           "struct.",
           bp::init<const Scalar, const Scalar, std::size_t, VerboseLevel,
-                   HessianApprox>(
+                   StepAcceptanceStrategy, HessianApprox>(
               ("self"_a, "tol", "mu_init"_a = 1e-2, "max_iters"_a = 1000,
                "verbose"_a = VerboseLevel::QUIET,
+               "sa_strategy"_a = StepAcceptanceStrategy::LINESEARCH_NONMONOTONE,
                "hess_approx"_a = HessianApprox::GAUSS_NEWTON)))
           .def("cycleProblem", &SolverType::cycleProblem,
                ("self"_a, "problem", "data"),
@@ -110,7 +113,7 @@ void exposeProxDDP() {
           .def_readwrite("max_al_iters", &SolverType::max_al_iters,
                          "Maximum number of AL iterations.")
           .def_readwrite("ls_mode", &SolverType::ls_mode, "Linesearch mode.")
-          .def_readwrite("sa_strategy", &SolverType::sa_strategy,
+          .def_readwrite("sa_strategy", &SolverType::sa_strategy_,
                          "StepAcceptance strategy.")
           .def_readwrite("rollout_type", &SolverType::rollout_type_,
                          "Rollout type.")
@@ -120,7 +123,6 @@ void exposeProxDDP() {
                          "Minimum regularization value.")
           .def_readwrite("reg_max", &SolverType::reg_max,
                          "Maximum regularization value.")
-          .def_readwrite("lq_print_detailed", &SolverType::lq_print_detailed)
           .def("updateLQSubproblem", &SolverType::updateLQSubproblem, "self"_a)
           .def("computeCriterion", &SolverType::computeCriterion, "self"_a,
                "Compute problem stationarity.")
@@ -143,6 +145,12 @@ void exposeProxDDP() {
                "(target_tol) will not be synced when the latter changes and "
                "`solver.run()` is called.")
           .def(SolverVisitor<SolverType>())
+          .add_property("linesearch",
+                        bp::make_function(
+                            +[](const SolverType &s) -> const ls_variant_t & {
+                              return s.linesearch_;
+                            },
+                            eigenpy::ReturnInternalVariant<ls_variant_t>{}))
           .def("run", &SolverType::run,
                ("self"_a, "problem", "xs_init"_a = bp::list(),
                 "us_init"_a = bp::list(), "vs_init"_a = bp::list(),
@@ -150,6 +158,12 @@ void exposeProxDDP() {
                "Run the algorithm. Can receive initial guess for "
                "multiplier trajectory.");
 
+  bp::class_<NonmonotoneLinesearch<Scalar>, bp::bases<Linesearch<Scalar>>>(
+      "NonmonotoneLinesearch", bp::no_init)
+      .def(bp::init<LsOptions>(("self"_a, "options")))
+      .def_readwrite("avg_eta", &NonmonotoneLinesearch<Scalar>::avg_eta)
+      .def_readwrite("beta_dec", &NonmonotoneLinesearch<Scalar>::beta_dec);
+
   {
     using AlmParams = SolverType::AlmParams;
     bp::scope scope{cls};
diff --git a/bindings/python/src/module.cpp b/bindings/python/src/module.cpp
index 113ee87e3..4800d09d1 100644
--- a/bindings/python/src/module.cpp
+++ b/bindings/python/src/module.cpp
@@ -42,7 +42,9 @@ static void exposeEnums() {
 
   bp::enum_<StepAcceptanceStrategy>("StepAcceptanceStrategy",
                                     "Step acceptance strategy.")
-      .value("SA_LINESEARCH", StepAcceptanceStrategy::LINESEARCH)
+      .value("SA_LINESEARCH_ARMIJO", StepAcceptanceStrategy::LINESEARCH_ARMIJO)
+      .value("SA_LINESEARCH_NONMONOTONE",
+             StepAcceptanceStrategy::LINESEARCH_NONMONOTONE)
       .value("SA_FILTER", StepAcceptanceStrategy::FILTER)
       .export_values();
 }
diff --git a/examples/acrobot.py b/examples/acrobot.py
index fe8ce0aec..84e520700 100644
--- a/examples/acrobot.py
+++ b/examples/acrobot.py
@@ -70,10 +70,10 @@ class Args(ArgsBase):
     )
 
 tol = 1e-3
-mu_init = 10.0
+mu_init = 1e-2
 solver = aligator.SolverProxDDP(tol, mu_init=mu_init, verbose=aligator.VERBOSE)
 solver.max_iters = 200
-solver.rollout_type = aligator.ROLLOUT_LINEAR
+solver.rollout_type = aligator.ROLLOUT_NONLINEAR
 solver.linear_solver_choice = aligator.LQ_SOLVER_STAGEDENSE
 solver.setup(problem)
 
@@ -96,7 +96,10 @@ class Args(ArgsBase):
     from aligator.utils.plotting import plot_controls_traj
 
     times = np.linspace(0, Tf, nsteps + 1)
-    fig1 = plot_controls_traj(times, res.us, ncols=1, rmodel=rmodel, figsize=(6.4, 3.2))
+    fig1, axes = plot_controls_traj(
+        times, res.us, ncols=1, rmodel=rmodel, figsize=(6.4, 3.2)
+    )
+    plt.title("Controls (N/m)")
     fig1.tight_layout()
     xs = np.stack(res.xs)
     vs = xs[:, nq:]
@@ -104,15 +107,17 @@ class Args(ArgsBase):
     theta_s = np.zeros((nsteps + 1, 2))
     theta_s0 = space.difference(space.neutral(), x0)[:2]
     theta_s = theta_s0 + np.cumsum(vs * timestep, axis=0)
-    fig2 = plt.figure(figsize=(6.4, 6.4))
-    plt.subplot(211)
+    fig2 = plt.figure(figsize=(6.4, 3.2))
+    plt.subplot(1, 2, 1)
     plt.plot(times, theta_s, label=("$\\theta_0$", "$\\theta_1$"))
-    plt.title("Joint angles")
+    plt.title("Joint angles (rad)")
+    plt.xlabel("Time (s)")
     plt.legend()
-    plt.subplot(212)
+    plt.subplot(1, 2, 2)
     plt.plot(times, xs[:, nq:], label=("$\\dot\\theta_0$", "$\\dot\\theta_1$"))
     plt.legend()
-    plt.title("Joint velocities")
+    plt.title("Joint velocities (rad/s)")
+    plt.xlabel("Time (s)")
     fig2.tight_layout()
 
     _fig_dict = {"controls": fig1, "velocities": fig2}
diff --git a/examples/cartpole.py b/examples/cartpole.py
index 0dc18757e..9a9bf039e 100644
--- a/examples/cartpole.py
+++ b/examples/cartpole.py
@@ -45,28 +45,27 @@ class Args(ArgsBase):
 
 # running cost regularizes the control input
 rcost = aligator.CostStack(space, nu)
-wu = np.ones(nu) * 1e-2
-rcost.addCost(aligator.QuadraticControlCost(space, np.zeros(nu), np.diag(wu) * dt))
-frame_place_target = pin.SE3.Identity()
-frame_place_target.translation[:] = target_pos
-frame_err = aligator.FramePlacementResidual(
+wu = np.ones(nu) * 1e-3
+wx_reg = np.eye(ndx) * 1e-3
+rcost.addCost(
+    "ureg", aligator.QuadraticControlCost(space, np.zeros(nu), np.diag(wu) * dt)
+)
+rcost.addCost(
+    "xreg", aligator.QuadraticStateCost(space, nu, space.neutral(), wx_reg * dt)
+)
+frame_err = aligator.FrameTranslationResidual(
     ndx,
     nu,
     model,
-    frame_place_target,
+    target_pos,
     frame_id,
 )
-weights_frame_place = np.zeros(6)
-weights_frame_place[:3] = 1.0
-weights_frame_place = np.diag(weights_frame_place)
-rcost.addCost(
-    aligator.QuadraticResidualCost(space, frame_err, weights_frame_place * dt)
-)
 term_cost = aligator.CostStack(space, nu)
+term_cost.addCost("xreg", aligator.QuadraticStateCost(space, nu, x0, wx_reg))
 
 # box constraint on control
-u_min = -6.0 * np.ones(nu)
-u_max = +6.0 * np.ones(nu)
+u_min = -2.0 * np.ones(nu)
+u_max = +2.0 * np.ones(nu)
 
 
 def get_box_cstr():
@@ -76,6 +75,7 @@ def get_box_cstr():
 
 nsteps = 500
 Tf = nsteps * dt
+print(f"Tf = {Tf}")
 problem = aligator.TrajOptProblem(x0, nu, space, term_cost)
 
 for i in range(nsteps):
@@ -84,23 +84,25 @@ def get_box_cstr():
         stage.addConstraint(*get_box_cstr())
     problem.addStage(stage)
 
-term_fun = aligator.FrameTranslationResidual(ndx, nu, model, target_pos, frame_id)
+term_fun = frame_err
 
 if args.term_cstr:
     problem.addTerminalConstraint(term_fun, constraints.EqualityConstraintSet())
 else:
+    weights_frame_place = 5 * np.ones(3)
+    weights_frame_place = np.diag(weights_frame_place)
     term_cost.addCost(
         aligator.QuadraticResidualCost(space, frame_err, weights_frame_place)
     )
 
 
-mu_init = 1e-2
+mu_init = 1e-8
 verbose = aligator.VerboseLevel.VERBOSE
-TOL = 1e-4
+TOL = 1e-6
 MAX_ITER = 300
 solver = aligator.SolverProxDDP(TOL, mu_init, max_iters=MAX_ITER, verbose=verbose)
-solver.rollout_type = aligator.ROLLOUT_LINEAR
-callback = aligator.HistoryCallback()
+solver.bcl_params.mu_lower_bound = 1e-11
+callback = aligator.HistoryCallback(solver)
 solver.registerCallback("his", callback)
 
 u0 = np.zeros(nu)
@@ -126,23 +128,25 @@ def get_box_cstr():
     ax1 = fig1.add_subplot(gs0[0])
     ax2 = fig1.add_subplot(gs0[1])
     lstyle = {"lw": 0.9}
-    ax1.plot(trange, xs_opt[:, 0], ls="-", **lstyle)
-    ax1.plot(trange, xs_opt[:, 2], ls="-", label="$\\dot{x}$", **lstyle)
-    ax1.set_ylabel("$q(t)$")
+    ax1.plot(trange, xs_opt[:, 0], ls="-", label="$x$ (m)", **lstyle)
+    ax1.plot(trange, xs_opt[:, 2], ls="-", label="$\\dot{x}$ (m/s)", **lstyle)
+    ax1.set_title("Cartpole position $x$")
     if args.term_cstr:
         pass
     ax1.legend()
-    ax2.plot(trange, xs_opt[:, 1], ls="-", **lstyle)
-    ax2.plot(trange, xs_opt[:, 3], ls="-", label="$\\dot{\\theta}$", **lstyle)
-    ax2.set_ylabel("Angle $\\theta(t)$")
+    ax2.plot(trange, xs_opt[:, 1], ls="-", label="$\\theta$ (rad)", **lstyle)
+    ax2.plot(trange, xs_opt[:, 3], ls="-", label="$\\dot{\\theta}$ (rad/s)", **lstyle)
+    ax2.set_title("Angle $\\theta(t)$")
     ax2.legend()
 
-    plt.xlabel("Time $t$")
+    plt.xlabel("Time (s)")
 
     gs1 = gs[1].subgridspec(1, 2, width_ratios=[1, 2])
     ax3 = plt.subplot(gs1[0])
     plt.plot(*_pts.T, ls=":")
     plt.scatter(*target_pos[1:], c="r", marker="^", zorder=2, label="EE target")
+    plt.xlabel("$x$ (m)")
+    plt.ylabel("$z$ (m)")
     plt.legend()
     ax3.set_aspect("equal")
     plt.title("Endpoint trajectory")
@@ -157,46 +161,17 @@ def get_box_cstr():
             colors="k",
             lw=2.5,
             alpha=0.4,
-            label=r"$\bar{u}$",
+            label=r"bound $\overline{u}$",
         )
-    plt.title("Controls $u(t)$")
+    plt.title(r"Controls $u$ (N/m)")
     plt.legend()
     fig1.tight_layout()
 
-    fig2 = plt.figure(figsize=(6.4, 4.8))
+    fig2 = plt.figure(figsize=(7.2, 4))
     ax: plt.Axes = plt.subplot(111)
     ax.hlines(TOL, 0, res.num_iters, lw=2.2, alpha=0.8, colors="k")
-    plot_convergence(callback, ax, res)
-    prim_tols = np.array(callback.prim_tols)
-    al_iters = np.array(callback.al_index)
-
-    itrange = np.arange(len(al_iters))
-    legends_ = [
-        "$\\epsilon_\\mathrm{tol}$",
-        "Prim. err $p$",
-        "Dual err $d$",
-    ]
-    if len(itrange) > 0:
-        ax.step(itrange, prim_tols, c="green", alpha=0.9, lw=1.1)
-        al_change = al_iters[1:] - al_iters[:-1]
-        al_change_idx = itrange[:-1][al_change > 0]
-        legends_.extend(
-            [
-                "Prim tol $\\eta_k$",
-                "AL iters",
-            ]
-        )
+    plot_convergence(callback, ax, res, show_al_iters=True)
 
-        ax.vlines(al_change_idx, *ax.get_ylim(), colors="gray", lw=4.0, alpha=0.5)
-    ax.legend(
-        [
-            "$\\epsilon_\\mathrm{tol}$",
-            "Prim. err $p$",
-            "Dual err $d$",
-            "Prim tol $\\eta_k$",
-            "AL iters",
-        ]
-    )
     fig2.tight_layout()
 
     fig_dict = {"traj": fig1, "conv": fig2}
@@ -222,7 +197,9 @@ def get_box_cstr():
     qs = [x[:nq] for x in res.xs.tolist()]
     vs = [x[nq:] for x in res.xs.tolist()]
 
-    obj = pin.GeometryObject("objective", 0, hppfcl.Sphere(0.05), frame_place_target)
+    obj = pin.GeometryObject(
+        "objective", 0, hppfcl.Sphere(0.05), pin.SE3(np.eye(3), target_pos)
+    )
     color = [255, 20, 83, 255]
     obj.meshColor[:] = color
     obj.meshColor /= 255
diff --git a/examples/lqr.py b/examples/lqr.py
index e17318fb5..5ad279acb 100644
--- a/examples/lqr.py
+++ b/examples/lqr.py
@@ -23,6 +23,12 @@ class Args(tap.Tap):
 args = Args().parse_args()
 np.random.seed(42)
 
+TAG = "LQR"
+if args.bounds:
+    TAG += "_bounded"
+if args.term_cstr:
+    TAG += "_cstr"
+
 nx = 3  # dimension of the state manifold
 nu = 3  # dimension of the input
 space = manifolds.VectorSpace(nx)
@@ -78,7 +84,7 @@ class Args(tap.Tap):
 tol = 1e-8
 solver = aligator.SolverProxDDP(tol, mu_init, verbose=verbose)
 
-his_cb = aligator.HistoryCallback()
+his_cb = aligator.HistoryCallback(solver)
 solver.registerCallback("his", his_cb)
 print("Registered callbacks:", solver.getCallbackNames().tolist())
 solver.max_iters = 20
@@ -98,6 +104,8 @@ class Args(tap.Tap):
 
 plt.subplot(121)
 fig1: plt.Figure = plt.gcf()
+fig1.set_figwidth(6.4)
+fig1.set_figheight(3.6)
 
 lstyle = {"lw": 0.9, "marker": ".", "markersize": 5}
 trange = np.arange(nsteps + 1)
@@ -144,7 +152,7 @@ class Args(tap.Tap):
 plt.tight_layout()
 
 
-fig2: plt.Figure = plt.figure()
+fig2: plt.Figure = plt.figure(figsize=(6.4, 3.6))
 ax: plt.Axes = fig2.add_subplot()
 niter = res.num_iters
 ax.hlines(
@@ -155,15 +163,13 @@ class Args(tap.Tap):
     linestyles="-",
     linewidth=2.0,
 )
-plot_convergence(his_cb, ax, res)
+plot_convergence(his_cb, ax, res, show_al_iters=True)
 ax.set_title("Convergence (constrained LQR)")
-ax.legend(
-    [
-        "Tolerance $\\epsilon_\\mathrm{tol}$",
-        "Primal error $p$",
-        "Dual error $d$",
-    ]
-)
 fig2.tight_layout()
+fig_dicts = {"traj": fig1, "conv": fig2}
+
+for name, _fig in fig_dicts.items():
+    _fig: plt.Figure
+    _fig.savefig(f"assets/{TAG}_{name}.pdf")
 
 plt.show()
diff --git a/examples/quadrotor_obstacles.py b/examples/quadrotor_obstacles.py
index 57a6082bd..e2a71e41c 100644
--- a/examples/quadrotor_obstacles.py
+++ b/examples/quadrotor_obstacles.py
@@ -322,15 +322,22 @@ def setup() -> aligator.TrajOptProblem:
         vizer = None
 
     tol = 1e-4
-    mu_init = 1.0
+    if args.bounds:
+        mu_init = 1e1
+        if args.obstacles:
+            mu_init = 1.0
+    # elif args.obstacles:
+    #     mu_init = 1e-2
+    else:
+        mu_init = 1e-6
     verbose = aligator.VerboseLevel.VERBOSE
-    history_cb = aligator.HistoryCallback()
     solver = aligator.SolverProxDDP(tol, mu_init, verbose=verbose)
+    history_cb = aligator.HistoryCallback(solver)
     if args.fddp:
         solver = aligator.SolverFDDP(tol, verbose=verbose)
     solver.max_iters = 400
+    solver.reg_min = 1e-5
     solver.registerCallback("his", history_cb)
-    solver.bcl_params.dyn_al_scale = 1e-6
     solver.setup(problem)
     solver.run(problem, xs_init, us_init)
 
@@ -351,42 +358,49 @@ def plot_costate_value() -> plt.Figure:
         plt.vlines(idx_switch, *plt.ylim(), colors="r", label="switch")
 
         plt.legend()
-        plt.xlabel("Time $t$")
+        plt.xlabel("Time $t$ (s)")
         plt.ylabel("Dimension")
         plt.title("Multipliers")
         plt.colorbar()
         plt.tight_layout()
         return plt.gcf()
 
+    TAG = "quadrotor"
     if args.obstacles:
-        TAG = "quadrotor_obstacles"
-    else:
-        TAG = "quadrotor"
+        TAG += "_obstacles"
+    if args.bounds:
+        TAG += "_bounds"
+    if args.term_cstr:
+        TAG += "_termcstr"
 
     root_pt_opt = np.stack(xs_opt)[:, :3]
     if args.plot:
+        from aligator.utils import plotting
+
         if len(results.lams) > 0:
             plot_costate_value()
 
         nplot = 3
-        fig: plt.Figure = plt.figure(figsize=(9.6, 5.4))
+        fig: plt.Figure = plt.figure(figsize=(7.2, 3.2))
         ax0: plt.Axes = fig.add_subplot(1, nplot, 1)
         ax0.plot(times[:-1], us_opt)
         ax0.hlines((u_min[0], u_max[0]), *times[[0, -1]], colors="k", alpha=0.3, lw=1.4)
-        ax0.set_title("Controls")
-        ax0.set_xlabel("Time")
+        ax0.set_title("Controls (N/m)")
+        ax0.set_xlabel("Time (s)")
         ax1: plt.Axes = fig.add_subplot(1, nplot, 2)
         ax1.plot(times, root_pt_opt)
+        ax1.set_xlabel("Time (s)")
+        ax1.set_title("Quadrotor position (m)")
         plt.legend(["$x$", "$y$", "$z$"])
         ax1.scatter([times_wp[-1]] * 3, x_term[:3], marker=".", c=["C0", "C1", "C2"])
         ax2: plt.Axes = fig.add_subplot(1, nplot, 3)
-        n_iter = np.arange(len(history_cb.prim_infeas.tolist()))
-        ax2.semilogy(
-            n_iter[1:], history_cb.prim_infeas.tolist()[1:], label="Primal err."
+        plotting.plot_convergence(
+            history_cb,
+            ax2,
+            res=results,
+            show_al_iters=True,
+            legend_kwargs=dict(fontsize=8),
         )
-        ax2.semilogy(n_iter, history_cb.dual_infeas.tolist(), label="Dual err.")
-        ax2.set_xlabel("Iterations")
-        ax2.legend()
 
         fig.tight_layout()
         for ext in ["png", "pdf"]:
diff --git a/examples/se2-car.cpp b/examples/se2-car.cpp
index 3e651874d..051e15321 100644
--- a/examples/se2-car.cpp
+++ b/examples/se2-car.cpp
@@ -9,7 +9,7 @@ int main() {
   const T mu_init = 1e-2;
   SolverProxDDPTpl<T> solver(1e-4, mu_init);
   solver.verbose_ = VERBOSE;
-  solver.sa_strategy = StepAcceptanceStrategy::FILTER;
+  solver.sa_strategy_ = StepAcceptanceStrategy::FILTER;
   solver.linear_solver_choice = LQSolverChoice::PARALLEL;
   solver.setNumThreads(4);
   solver.rollout_type_ = RolloutType::LINEAR;
diff --git a/examples/solo_jump.py b/examples/solo_jump.py
index e2b441aae..4045db448 100644
--- a/examples/solo_jump.py
+++ b/examples/solo_jump.py
@@ -30,6 +30,7 @@ class Args(ArgsBase):
 
 
 args = Args().parse_args()
+q0[2] += 0.02
 pin.framesForwardKinematics(rmodel, rdata, q0)
 
 
@@ -42,7 +43,7 @@ class Args(ArgsBase):
 effort_limit = rmodel.effortLimit[6:]
 print(f"Effort limit: {effort_limit}")
 
-constraint_models = create_ground_contact_model(rmodel, (0, 0, 100), 50)
+constraint_models = create_ground_contact_model(rmodel, (0, 0, 100), 60)
 prox_settings = pin.ProximalSettings(1e-9, 1e-10, 10)
 ode1 = dynamics.MultibodyConstraintFwdDynamics(
     space, act_matrix, constraint_models, prox_settings
@@ -64,34 +65,29 @@ def test():
 test()
 
 
-dt = 20e-3  # 20 ms
+dt = 5e-3  # 20 ms
 tf = 1.2  # in seconds
 nsteps = int(tf / dt)
 print("Num steps: {:d}".format(nsteps))
 
 switch_t0 = 0.4
-switch_t1 = 0.9  # landing time
+switch_t1 = 1.0  # landing time
 k0 = int(switch_t0 / dt)
 k1 = int(switch_t1 / dt)
 
 times = np.linspace(0, tf, nsteps + 1)
 mask = (switch_t0 <= times) & (times < switch_t1)
 
-x0_ref = np.concatenate((q0, np.zeros(nv)))
-x_ref_flight = x0_ref.copy()
+q1 = q0.copy()
+# q1[3:7] = pin.exp3_quat(np.array([0.0, 0.0, np.pi / 3]))
+v0 = np.zeros(nv)
+x0_ref = np.concatenate((q0, v0))
 w_x = np.ones(space.ndx) * 1e-2
-w_x[:6] = 0.0
+w_x[:nv] = 1.0
+w_x[3:6] = 0.1
 w_x[nv : nv + 6] = 0.0
 w_x = np.diag(w_x)
-w_u = np.eye(nu) * 1e-4
-
-
-def add_fly_high_cost(costs: aligator.CostStack, slope):
-    fly_high_w = 1.0
-    for fname, fid in FOOT_FRAME_IDS.items():
-        fn = aligator.FlyHighResidual(space.ndx, rmodel, fid, slope, nu)
-        fl_cost = aligator.QuadraticResidualCost(space, fn, np.eye(2) * dt)
-        costs.addCost(fl_cost, fly_high_w / len(FOOT_FRAME_IDS))
+w_u = np.eye(nu) * 1e-1
 
 
 def create_land_fns():
@@ -99,7 +95,7 @@ def create_land_fns():
     for fname, fid in FOOT_FRAME_IDS.items():
         p_ref = rdata.oMf[fid].translation
         fn = aligator.FrameTranslationResidual(space.ndx, nu, rmodel, p_ref, fid)
-        out[fid] = fn[2]
+        out[fid] = fn[2]  # [2]
     return out
 
 
@@ -122,21 +118,18 @@ def create_land_cost(costs, w):
         costs.addCost(land_cost, w / len(FOOT_FRAME_IDS))
 
 
-x_ref_flight[2] = 1.2
 stages = []
 for k in range(nsteps):
     vf = ode1
-    wxlocal_k = w_x * dt
     if mask[k]:
         vf = ode2
-    xref = x0_ref
+    xref = x0_ref.copy()
 
-    xreg_cost = aligator.QuadraticStateCost(space, nu, xref, weights=wxlocal_k)
+    xreg_cost = aligator.QuadraticStateCost(space, nu, xref, weights=w_x * dt)
     ureg_cost = aligator.QuadraticControlCost(space, nu, weights=w_u * dt)
     cost = aligator.CostStack(space, nu)
     cost.addCost(xreg_cost)
     cost.addCost(ureg_cost)
-    add_fly_high_cost(cost, slope=50)
 
     dyn_model = dynamics.IntegratorSemiImplEuler(vf, dt)
     stm = aligator.StageModel(cost, dyn_model)
@@ -147,8 +140,8 @@ def create_land_cost(costs, w):
             constraints.BoxConstraint(-effort_limit, effort_limit),
         )
     if k == k1:
-        fns = create_land_fns()
-        for fid, fn in fns.items():
+        pin.framesForwardKinematics(rmodel, rdata, q1)
+        for fid, fn in create_land_fns().items():
             stm.addConstraint(fn, constraints.EqualityConstraintSet())
         for fid, fn in create_land_vel_fns().items():
             stm.addConstraint(fn, constraints.EqualityConstraintSet())
@@ -156,19 +149,20 @@ def create_land_cost(costs, w):
     stages.append(stm)
 
 
-w_xterm = w_x.copy()
-term_cost = aligator.QuadraticStateCost(space, nu, x0_ref, weights=w_x)
+w_xterm = w_x * 1
+xterm = np.concatenate((q1, v0))
+print("x0   :", x0_ref)
+print("xterm:", xterm)
+term_cost = aligator.QuadraticStateCost(space, nu, xterm, weights=w_xterm)
 
 problem = aligator.TrajOptProblem(x0_ref, stages, term_cost)
 mu_init = 1e-5
-tol = 1e-4
-solver = aligator.SolverProxDDP(tol, mu_init, verbose=aligator.VERBOSE, max_iters=100)
+tol = 1e-5
+solver = aligator.SolverProxDDP(tol, mu_init, verbose=aligator.VERBOSE, max_iters=300)
 solver.rollout_type = aligator.ROLLOUT_LINEAR
-solver.linear_solver_choice = aligator.LQ_SOLVER_PARALLEL
-# solver.sa_strategy = aligator.SA_FILTER
 solver.setNumThreads(args.num_threads)
 
-cb_ = aligator.HistoryCallback()
+cb_ = aligator.HistoryCallback(solver)
 solver.registerCallback("his", cb_)
 solver.setup(problem)
 
@@ -207,7 +201,8 @@ def make_plots(res: aligator.Results):
 
     fig4 = plt.figure()
     ax = fig4.add_subplot(111)
-    plot_convergence(cb_, ax, res=res)
+    ax.hlines(tol, 0, res.num_iters, lw=2.2, alpha=0.8, colors="k")
+    plot_convergence(cb_, ax, res, show_al_iters=True)
     fig4.tight_layout()
 
     _fig_dict = {"controls": fig1, "velocities": fig2, "foot_traj": fig3, "conv": fig4}
@@ -228,7 +223,9 @@ def make_plots(res: aligator.Results):
             visual_model=robot.visual_model,
             data=rdata,
         )
-        vizer.initViewer(loadModel=True, zmq_url=args.zmq_url)
+        vizer.initViewer(
+            open=args.zmq_url is None, loadModel=True, zmq_url=args.zmq_url
+        )
         # custom_color = np.asarray((53, 144, 243)) / 255.0
         # vizer.setBackgroundColor(col_bot=list(custom_color), col_top=(1, 1, 1, 1))
         manage_lights(vizer)
@@ -249,7 +246,8 @@ def make_plots(res: aligator.Results):
     qs = xs[:, :nq]
     vs = xs[:, nq:]
 
-    FPS = min(30, 1.0 / dt)
+    # FPS = min(30, 1.0 / dt)
+    FPS = 1.0 / dt
 
     if args.display:
         import contextlib
diff --git a/examples/talos-walk.cpp b/examples/talos-walk.cpp
index 315395152..98c9143d4 100644
--- a/examples/talos-walk.cpp
+++ b/examples/talos-walk.cpp
@@ -29,7 +29,7 @@ int main(int, char **) {
   us_i.assign(nsteps, u0);
 
   solver.rollout_type_ = aligator::RolloutType::LINEAR;
-  solver.sa_strategy = aligator::StepAcceptanceStrategy::FILTER;
+  solver.sa_strategy_ = aligator::StepAcceptanceStrategy::FILTER;
   solver.filter_.beta_ = 1e-5;
   solver.force_initial_condition_ = true;
   solver.reg_min = 1e-6;
diff --git a/examples/talos_arms.py b/examples/talos_arms.py
index 54dd055c1..2a217c95e 100644
--- a/examples/talos_arms.py
+++ b/examples/talos_arms.py
@@ -90,7 +90,9 @@ class Args(ArgsBase):
 solver.rollout_type = aligator.ROLLOUT_NONLINEAR
 # solver = aligator.SolverFDDP(TOL, verbose=verbose)
 solver.max_iters = max_iters
-solver.sa_strategy = aligator.SA_LINESEARCH  # FILTER or LINESEARCH
+solver.sa_strategy = (
+    aligator.SA_LINESEARCH_NONMONOTONE
+)  # FILTER or LINESEARCH_ARMIJO or LINESEARCH_NONMONOTONE
 solver.setup(problem)
 
 u0 = compute_quasistatic(rmodel, rdata, x0, acc=np.zeros(nv))
diff --git a/examples/ur10_ballistic.py b/examples/ur10_ballistic.py
index 2a4e4dea7..47f612c8d 100644
--- a/examples/ur10_ballistic.py
+++ b/examples/ur10_ballistic.py
@@ -9,7 +9,11 @@
 from pathlib import Path
 from typing import Tuple
 from pinocchio.visualize import MeshcatVisualizer
-from aligator.utils.plotting import plot_controls_traj, plot_velocity_traj
+from aligator.utils.plotting import (
+    plot_controls_traj,
+    plot_convergence,
+    plot_velocity_traj,
+)
 from utils import (
     add_namespace_prefix_to_models,
     ArgsBase,
@@ -31,14 +35,16 @@ class Args(ArgsBase):
 print(f"Velocity limit (before): {robot.model.velocityLimit}")
 
 
-def load_projectile_model():
+def load_projectile_model(free_flyer: bool = True):
     ball_urdf = Path(__file__).parent / "mug.urdf"
     packages_dirs = [str(Path(__file__).parent)]
     ball_scale = 1.0
     model, cmodel, vmodel = pin.buildModelsFromUrdf(
         str(ball_urdf),
         package_dirs=packages_dirs,
-        root_joint=pin.JointModelFreeFlyer(),
+        root_joint=pin.JointModelFreeFlyer()
+        if free_flyer
+        else pin.JointModelTranslation(),
     )
     print("Projectile model:\n", model)
     for geom in cmodel.geometryObjects:
@@ -76,21 +82,23 @@ def append_ball_to_robot_model(
     return rmodel, cmodel, vmodel, ref_q0
 
 
+nq_o = robot.model.nq
+nv_o = robot.model.nv
 rmodel, cmodel, vmodel, ref_q0 = append_ball_to_robot_model(robot)
 print(f"New model velocity lims: {rmodel.velocityLimit}")
 space = manifolds.MultibodyPhaseSpace(rmodel)
 rdata: pin.Data = rmodel.createData()
-nq = rmodel.nq
-nv = rmodel.nv
-nu = nv - 6
+nq_b = rmodel.nq
+nv_b = rmodel.nv
+nu = nv_b - 6
 ndx = space.ndx
 x0 = space.neutral()
-x0[:nq] = ref_q0
+x0[:nq_b] = ref_q0
 print("X0 = {}".format(x0))
-MUG_VEL_IDX = slice(robot.nv, nv)
+MUG_VEL_IDX = slice(robot.nv, nv_b)
 
 
-def create_rcm():
+def create_rcm(contact_type=pin.ContactType.CONTACT_6D):
     # create rigid constraint between ball & tool0
     tool_fid = rmodel.getFrameId("tool0")
     frame: pin.Frame = rmodel.frames[tool_fid]
@@ -100,7 +108,7 @@ def create_rcm():
     pl1 = rmodel.frames[tool_fid].placement
     pl2 = rdata.oMf[tool_fid]
     rcm = pin.RigidConstraintModel(
-        pin.ContactType.CONTACT_6D,
+        contact_type,
         rmodel,
         joint1_id,
         pl1,
@@ -133,16 +141,10 @@ def configure_viz(target_pos):
 
 target_pos = np.array([2.4, -0.2, 0.0])
 
-if args.display:
-    viz = configure_viz(target_pos=target_pos)
-    viz.display(ref_q0)
-else:
-    viz = None
-
 dt = 0.01
 tf = 2.0  # seconds
 nsteps = int(tf / dt)
-actuation_matrix = np.eye(nv, nu)
+actuation_matrix = np.eye(nv_b, nu)
 
 prox_settings = pin.ProximalSettings(accuracy=1e-8, mu=1e-6, max_iter=20)
 rcm = create_rcm()
@@ -153,8 +155,8 @@ def configure_viz(target_pos):
 dyn_model1 = dynamics.IntegratorSemiImplEuler(ode1, dt)
 dyn_model2 = dynamics.IntegratorSemiImplEuler(ode2, dt)
 
-q0 = x0[:nq]
-v0 = x0[nq:]
+q0 = x0[:nq_b]
+v0 = x0[nq_b:]
 u0_free = pin.rnea(robot.model, robot.data, robot.q0, robot.v0, robot.v0)
 u0, lam_c = aligator.underactuatedConstrainedInverseDynamics(
     rmodel, rdata, q0, v0, actuation_matrix, [rcm], [rcm.createData()]
@@ -178,16 +180,19 @@ def testu0(u0):
 dms = [dyn_model1] * nsteps
 us_i = [u0] * len(dms)
 xs_i = aligator.rollout(dms, x0, us_i)
-qs_i = [x[:nq] for x in xs_i]
+qs_i = [x[:nq_b] for x in xs_i]
 
 if args.display:
+    viz = configure_viz(target_pos=target_pos)
     viz.play(qs_i, dt=dt)
+else:
+    viz = None
 
 
 def create_running_cost():
     costs = aligator.CostStack(space, nu)
-    w_x = np.array([1e-3] * nv + [0.1] * nv)
-    w_v = w_x[nv:]
+    w_x = np.array([1e-3] * nv_b + [0.1] * nv_b)
+    w_v = w_x[nv_b:]
     # no costs on mug
     w_x[MUG_VEL_IDX] = 0.0
     w_v[MUG_VEL_IDX] = 0.0
@@ -203,7 +208,7 @@ def create_running_cost():
 def create_term_cost(has_frame_cost=False, w_ball=1.0):
     w_xf = np.zeros(ndx)
     w_xf[: robot.nv] = 1e-4
-    w_xf[nv + 6 :] = 1e-6
+    w_xf[nv_b + 6 :] = 1e-6
     costs = aligator.CostStack(space, nu)
     xreg = aligator.QuadraticStateCost(space, nu, x0, np.diag(w_xf))
     costs.addCost(xreg)
@@ -234,11 +239,16 @@ def get_position_limit_constraint():
     return (pos_fn, box_cstr)
 
 
+JOINT_VEL_LIM_IDX = [0, 1, 3, 4, 5, 6]
+print("Joint vel. limits enforced for:")
+for i in JOINT_VEL_LIM_IDX:
+    print(robot.model.names[i])
+
+
 def get_velocity_limit_constraint():
     state_fn = aligator.StateErrorResidual(space, nu, space.neutral())
-    idx = [1, 3, 4, 5]
-    vel_fn = state_fn[[nv + i for i in idx]]
-    vlim = rmodel.velocityLimit[idx]
+    vel_fn = state_fn[[nv_b + i for i in JOINT_VEL_LIM_IDX]]
+    vlim = rmodel.velocityLimit[JOINT_VEL_LIM_IDX]
     assert vel_fn.nr == vlim.shape[0]
     box_cstr = constraints.BoxConstraint(-vlim, vlim)
     return (vel_fn, box_cstr)
@@ -272,12 +282,11 @@ def create_stage(contact: bool):
 problem.addTerminalConstraint(*create_term_constraint(target_pos))
 problem.addTerminalConstraint(*get_velocity_limit_constraint())
 tol = 1e-4
-mu_init = 1e-1
+mu_init = 2e-1
 solver = aligator.SolverProxDDP(tol, mu_init, max_iters=300, verbose=aligator.VERBOSE)
 # solver.linear_solver_choice = aligator.LQ_SOLVER_PARALLEL
 # solver.rollout_type = aligator.ROLLOUT_LINEAR
-# solver.sa_strategy = aligator.SA_FILTER
-his_cb = aligator.HistoryCallback()
+his_cb = aligator.HistoryCallback(solver)
 solver.setNumThreads(4)
 solver.registerCallback("his", his_cb)
 solver.setup(problem)
@@ -290,8 +299,8 @@ def create_stage(contact: bool):
 
 xs = solver.results.xs
 us = solver.results.us
-qs = [x[:nq] for x in xs]
-vs = [x[nq:] for x in xs]
+qs = [x[:nq_b] for x in xs]
+vs = [x[nq_b:] for x in xs]
 vs = np.asarray(vs)
 proj_frame_id = rmodel.getFrameId("ball/root_joint")
 
@@ -311,7 +320,7 @@ def get_frame_vel(k: int):
 if args.display:
 
     def viz_callback(i: int):
-        pin.forwardKinematics(rmodel, rdata, qs[i], xs[i][nq:])
+        pin.forwardKinematics(rmodel, rdata, qs[i], xs[i][nq_b:])
         viz.drawFrameVelocities(proj_frame_id, v_scale=0.06)
         fid = rmodel.getFrameId("ball/root_joint")
         ctar: pin.SE3 = rdata.oMf[fid]
@@ -336,18 +345,19 @@ def viz_callback(i: int):
     _joint_names = robot.model.names
     _efflims = robot.model.effortLimit
     _vlims = robot.model.velocityLimit
+    for i in range(nv_o):
+        if i not in JOINT_VEL_LIM_IDX:
+            _vlims[i] = np.inf
+    figsize = (6.4, 4.0)
     fig1, _ = plot_controls_traj(
-        times, us, joint_names=_joint_names, effort_limit=_efflims
+        times, us, rmodel=rmodel, effort_limit=_efflims, figsize=figsize
     )
+    fig1.suptitle("Controls (N/m)")
     fig2, _ = plot_velocity_traj(
-        times, vs[:, :-6], rmodel=robot.model, vel_limit=_vlims
+        times, vs[:, :-6], rmodel=robot.model, vel_limit=_vlims, figsize=figsize
     )
 
-    for fig, name in [(fig1, "controls"), (fig2, "velocity")]:
-        PLOTDIR = Path("assets")
-        for ext in [".png", ".pdf"]:
-            figpath: Path = PLOTDIR / f"{EXPERIMENT_NAME}_{name}"
-            fig.savefig(figpath.with_suffix(ext))
+    PLOTDIR = Path("assets")
 
     fig3 = plt.figure()
     ax: plt.Axes = fig3.add_subplot(111)
@@ -355,4 +365,22 @@ def viz_callback(i: int):
     ax.set_yscale("log")
     ax.set_title("Dynamic slack errors $\\|s\\|_\\infty$")
 
+    fig4 = plt.figure(figsize=(6.4, 3.6))
+    ax = fig4.add_subplot(111)
+    plot_convergence(
+        his_cb,
+        ax,
+        res=solver.results,
+        show_al_iters=True,
+        legend_kwargs=dict(fontsize=8),
+    )
+    ax.set_title("Convergence")
+    fig4.tight_layout()
+
+    _fig_dict = {"controls": fig1, "velocity": fig2, "conv": fig4}
+    for name, fig in _fig_dict.items():
+        for ext in [".png", ".pdf"]:
+            figpath: Path = PLOTDIR / f"{EXPERIMENT_NAME}_{name}"
+            fig.savefig(figpath.with_suffix(ext))
+
     plt.show()
diff --git a/examples/ur5_reach.py b/examples/ur5_reach.py
index 4272c2442..a0ae7620a 100644
--- a/examples/ur5_reach.py
+++ b/examples/ur5_reach.py
@@ -122,10 +122,10 @@ def computeQuasistatic(model: pin.Model, x0, a):
 max_iters = 40
 solver = aligator.SolverProxDDP(tol, mu_init, max_iters=max_iters, verbose=verbose)
 solver.rollout_type = aligator.ROLLOUT_NONLINEAR
-solver.sa_strategy = aligator.SA_LINESEARCH
+solver.sa_strategy = aligator.SA_LINESEARCH_NONMONOTONE
 if args.fddp:
     solver = aligator.SolverFDDP(tol, verbose, max_iters=max_iters)
-cb = aligator.HistoryCallback()
+cb = aligator.HistoryCallback(solver)
 solver.registerCallback("his", cb)
 solver.setup(problem)
 solver.run(problem, init_xs, init_us)
diff --git a/examples/utils/solo.py b/examples/utils/solo.py
index 55de49ed7..30cd1bead 100644
--- a/examples/utils/solo.py
+++ b/examples/utils/solo.py
@@ -7,7 +7,7 @@
 rmodel: pin.Model = robot.model
 rdata: pin.Data = robot.data
 stance_name = "straight_standing"
-q0 = rmodel.referenceConfigurations[stance_name]
+q0 = rmodel.referenceConfigurations[stance_name].copy()
 
 FOOT_FRAME_IDS = {
     fname: rmodel.getFrameId(fname)
diff --git a/include/aligator/core/enums.hpp b/include/aligator/core/enums.hpp
index 3fc9afe02..5d7c783d7 100644
--- a/include/aligator/core/enums.hpp
+++ b/include/aligator/core/enums.hpp
@@ -26,6 +26,10 @@ enum struct MultiplierUpdateMode { NEWTON, PRIMAL, PRIMAL_DUAL };
 enum struct LinesearchMode { PRIMAL = 0, PRIMAL_DUAL = 1 };
 
 /// Whether to use linesearch or filter during step acceptance phase
-enum struct StepAcceptanceStrategy { LINESEARCH = 0, FILTER = 1 };
+enum struct StepAcceptanceStrategy {
+  LINESEARCH_ARMIJO,
+  LINESEARCH_NONMONOTONE,
+  FILTER,
+};
 
 } // namespace aligator
diff --git a/include/aligator/core/linesearch-nonmonotone.hpp b/include/aligator/core/linesearch-nonmonotone.hpp
new file mode 100644
index 000000000..57b9224b4
--- /dev/null
+++ b/include/aligator/core/linesearch-nonmonotone.hpp
@@ -0,0 +1,63 @@
+#pragma once
+
+#include <proxsuite-nlp/linesearch-base.hpp>
+#include <functional>
+
+namespace aligator {
+using proxsuite::nlp::Linesearch;
+using proxsuite::nlp::LinesearchStrategy;
+
+/// @brief Nonmonotone Linesearch algorithm. Modifies the Armijo condition with
+/// a moving average of function values.
+/// @details This is the algorithm from Zhang and Hager, SiOpt 2004.
+template <typename Scalar> struct NonmonotoneLinesearch : Linesearch<Scalar> {
+  using typename Linesearch<Scalar>::FunctionSample;
+  using typename Linesearch<Scalar>::Options;
+  using fun_t = std::function<Scalar(Scalar)>;
+
+  Scalar run(fun_t f, Scalar phi0, Scalar dphi0, Scalar &a_opt);
+  NonmonotoneLinesearch(const Options &options);
+
+  void reset() {
+    mov_avg = Scalar(0.);
+    avg_weight = Scalar(0.);
+  }
+
+  /// Weight for moving average
+  Scalar avg_eta = 0.85;
+  Scalar beta_dec = 0.5;
+
+private:
+  Scalar mov_avg;
+  Scalar avg_weight;
+};
+
+template <typename Scalar>
+NonmonotoneLinesearch<Scalar>::NonmonotoneLinesearch(const Options &options)
+    : Linesearch<Scalar>(options), mov_avg(0.), avg_weight(0.) {}
+
+template <typename Scalar>
+Scalar NonmonotoneLinesearch<Scalar>::run(fun_t f, Scalar phi0, Scalar dphi0,
+                                          Scalar &a_opt) {
+  const Options &opts = this->options_;
+  mov_avg = avg_eta * avg_weight * mov_avg + phi0;
+  avg_weight = avg_eta * avg_weight + 1;
+  mov_avg /= avg_weight;
+
+  while (a_opt > opts.alpha_min) {
+    try {
+      const Scalar phia = f(a_opt);
+      bool suff_decrease = phia <= mov_avg + opts.armijo_c1 * a_opt * dphi0;
+      if (suff_decrease)
+        return phia;
+    } catch (const std::runtime_error &) {
+    }
+    a_opt *= beta_dec;
+  }
+
+  // then, a_opt <= opts.alpha_min
+  a_opt = std::max(a_opt, opts.alpha_min);
+  return f(a_opt);
+}
+
+} // namespace aligator
diff --git a/include/aligator/helpers/history-callback.hpp b/include/aligator/helpers/history-callback.hpp
index 87e20e04e..135060bc8 100644
--- a/include/aligator/helpers/history-callback.hpp
+++ b/include/aligator/helpers/history-callback.hpp
@@ -5,7 +5,8 @@
 #include "aligator/core/workspace-base.hpp"
 #include "aligator/core/results-base.hpp"
 
-#include "aligator/solvers/proxddp/results.hpp"
+#include <typeindex>
+#include <any>
 
 namespace aligator {
 
@@ -13,10 +14,11 @@ namespace aligator {
 template <typename Scalar> struct HistoryCallbackTpl : CallbackBaseTpl<Scalar> {
   using Workspace = WorkspaceBaseTpl<Scalar>;
   using Results = ResultsBaseTpl<Scalar>;
-  HistoryCallbackTpl(bool store_pd_vars = false, bool store_values = true,
-                     bool store_residuals = true)
+  template <typename Solver>
+  HistoryCallbackTpl(Solver *solver, bool store_pd_vars = false,
+                     bool store_values = true)
       : store_primal_dual_vars_(store_pd_vars), store_values_(store_values),
-        store_residuals_(store_residuals) {}
+        rtti_(typeid(*solver)), solver_(solver) {}
 
   ALIGATOR_DYNAMIC_TYPEDEFS(Scalar);
 
@@ -32,31 +34,14 @@ template <typename Scalar> struct HistoryCallbackTpl : CallbackBaseTpl<Scalar> {
   std::vector<Scalar> prim_tols;
   std::vector<Scalar> dual_tols;
 
-  void call(const Workspace & /*workspace*/, const Results &results) {
-    if (store_primal_dual_vars_) {
-      xs.push_back(results.xs);
-      us.push_back(results.us);
-      // lams.push_back(results.lams);
-    }
-    if (store_values_) {
-      values.push_back(results.traj_cost_);
-      merit_values.push_back(results.merit_value_);
-    }
-    if (store_residuals_) {
-      prim_infeas.push_back(results.prim_infeas);
-      dual_infeas.push_back(results.dual_infeas);
-    }
-    // if (auto w = dynamic_cast<const WorkspaceTpl<Scalar> *>(&workspace)) {
-    //   inner_crits.push_back(w->inner_criterion);
-    // }
-    if (auto r = dynamic_cast<const ResultsTpl<Scalar> *>(&results)) {
-      al_index.push_back(r->al_iter);
-    }
-  }
+  void call(const Workspace & /*workspace*/, const Results &results);
 
   bool store_primal_dual_vars_;
   bool store_values_;
-  bool store_residuals_;
+
+private:
+  std::type_index rtti_;
+  std::any solver_;
 };
 
 } // namespace aligator
diff --git a/include/aligator/helpers/history-callback.hxx b/include/aligator/helpers/history-callback.hxx
new file mode 100644
index 000000000..4e0dc1658
--- /dev/null
+++ b/include/aligator/helpers/history-callback.hxx
@@ -0,0 +1,35 @@
+#include "history-callback.hpp"
+
+#include "aligator/solvers/proxddp/solver-proxddp.hpp"
+
+namespace aligator {
+
+template <typename Scalar>
+void HistoryCallbackTpl<Scalar>::call(const Workspace & /*workspace*/,
+                                      const Results &results) {
+  if (store_primal_dual_vars_) {
+    xs.push_back(results.xs);
+    us.push_back(results.us);
+    // lams.push_back(results.lams);
+  }
+  if (store_values_) {
+    values.push_back(results.traj_cost_);
+    merit_values.push_back(results.merit_value_);
+  }
+  prim_infeas.push_back(results.prim_infeas);
+  dual_infeas.push_back(results.dual_infeas);
+  // if (auto w = dynamic_cast<const WorkspaceTpl<Scalar> *>(&workspace)) {
+  //   inner_crits.push_back(w->inner_criterion);
+  // }
+  if (auto r = dynamic_cast<const ResultsTpl<Scalar> *>(&results)) {
+    al_index.push_back(r->al_iter);
+  }
+
+  if (rtti_ == typeid(SolverProxDDPTpl<Scalar>)) {
+    auto *s = std::any_cast<SolverProxDDPTpl<Scalar> *>(solver_);
+    prim_tols.push_back(s->prim_tol_);
+    dual_tols.push_back(s->inner_tol_);
+  }
+}
+
+} // namespace aligator
diff --git a/include/aligator/overloads.hpp b/include/aligator/overloads.hpp
new file mode 100644
index 000000000..0a830e524
--- /dev/null
+++ b/include/aligator/overloads.hpp
@@ -0,0 +1,11 @@
+#pragma once
+
+namespace aligator {
+
+/// @brief Utility helper struct for creating visitors from lambdas.
+template <typename... Ts> struct overloads : Ts... {
+  using Ts::operator()...;
+};
+template <class... Ts> overloads(Ts...) -> overloads<Ts...>;
+
+} // namespace aligator
diff --git a/include/aligator/solvers/proxddp/solver-proxddp.hpp b/include/aligator/solvers/proxddp/solver-proxddp.hpp
index bc2c3583f..274b04b2e 100644
--- a/include/aligator/solvers/proxddp/solver-proxddp.hpp
+++ b/include/aligator/solvers/proxddp/solver-proxddp.hpp
@@ -3,7 +3,9 @@
 /// @copyright Copyright (C) 2022-2024 LAAS-CNRS, INRIA
 #pragma once
 
+#include "aligator/overloads.hpp"
 #include "aligator/core/linesearch.hpp"
+#include "aligator/core/linesearch-nonmonotone.hpp"
 #include "aligator/core/filter.hpp"
 #include "aligator/core/callback-base.hpp"
 #include "aligator/core/enums.hpp"
@@ -14,6 +16,7 @@
 #include "results.hpp"
 
 #include <boost/unordered_map.hpp>
+#include <variant>
 
 namespace aligator {
 namespace gar {
@@ -32,8 +35,6 @@ enum class LQSolverChoice { SERIAL, PARALLEL, STAGEDENSE };
 /// implementation.
 template <typename _Scalar> struct SolverProxDDPTpl {
 public:
-  // typedefs
-
   using Scalar = _Scalar;
   ALIGATOR_DYNAMIC_TYPEDEFS(Scalar);
   using Problem = TrajOptProblemTpl<Scalar>;
@@ -50,8 +51,53 @@ template <typename _Scalar> struct SolverProxDDPTpl {
   using CstrSet = ConstraintSetTpl<Scalar>;
   using TrajOptData = TrajOptDataTpl<Scalar>;
   using LinesearchOptions = typename Linesearch<Scalar>::Options;
-  using LinesearchType = proxsuite::nlp::ArmijoLinesearch<Scalar>;
-  using Filter = FilterTpl<Scalar>;
+
+  struct LinesearchVariant {
+    using fun_t = std::function<Scalar(Scalar)>;
+    using variant_t = std::variant<std::monostate, ArmijoLinesearch<Scalar>,
+                                   NonmonotoneLinesearch<Scalar>>;
+
+    Scalar run(const fun_t &fun, const Scalar phi0, const Scalar dphi0,
+               Scalar &alpha_try) {
+      return std::visit(
+          overloads{[](std::monostate &) {
+                      return std::numeric_limits<Scalar>::quiet_NaN();
+                    },
+                    [&](auto &&method) {
+                      return method.run(fun, phi0, dphi0, alpha_try);
+                    }},
+          impl_);
+    }
+
+    void reset() {
+      std::visit(overloads{[](std::monostate &) {},
+                           [&](auto &&method) { method.reset(); }},
+                 impl_);
+    }
+
+    Scalar isValid() const { return impl_.index() > 0ul; }
+
+    operator const variant_t &() const { return impl_; }
+
+  private:
+    explicit LinesearchVariant() {}
+    void init(StepAcceptanceStrategy strat, const LinesearchOptions &options) {
+      switch (strat) {
+      case StepAcceptanceStrategy::LINESEARCH_ARMIJO:
+        impl_ = ArmijoLinesearch<Scalar>(options);
+        break;
+      case StepAcceptanceStrategy::LINESEARCH_NONMONOTONE:
+        impl_ = NonmonotoneLinesearch<Scalar>(options);
+        break;
+      default:
+        ALIGATOR_WARNING("LinesearchVariant::",
+                         "provided StepAcceptanceStrategy is invalid.");
+        break;
+      }
+    }
+    friend SolverProxDDPTpl;
+    variant_t impl_;
+  };
 
   struct AlmParams {
     /// Log-factor \f$\alpha_\eta\f$ for primal tolerance (failure)
@@ -113,13 +159,10 @@ template <typename _Scalar> struct SolverProxDDPTpl {
   VerboseLevel verbose_;
   /// Choice of linear solver
   LQSolverChoice linear_solver_choice = LQSolverChoice::SERIAL;
-  bool lq_print_detailed = false;
   /// Type of Hessian approximation. Default is Gauss-Newton.
   HessianApprox hess_approx_ = HessianApprox::GAUSS_NEWTON;
   /// Linesearch options, as in proxsuite-nlp.
   LinesearchOptions ls_params;
-  /// Type of linesearch strategy. Default is Armijo.
-  LinesearchStrategy ls_strat = LinesearchStrategy::ARMIJO;
   /// Type of Lagrange multiplier update.
   MultiplierUpdateMode multiplier_update_mode = MultiplierUpdateMode::NEWTON;
   /// Linesearch mode.
@@ -131,7 +174,7 @@ template <typename _Scalar> struct SolverProxDDPTpl {
   /// Parameters for the BCL outer loop of the augmented Lagrangian algorithm.
   AlmParams bcl_params;
   /// Step acceptance mode.
-  StepAcceptanceStrategy sa_strategy = StepAcceptanceStrategy::LINESEARCH;
+  StepAcceptanceStrategy sa_strategy_;
 
   /// Force the initial state @f$ x_0 @f$ to be fixed to the problem initial
   /// condition.
@@ -148,9 +191,9 @@ template <typename _Scalar> struct SolverProxDDPTpl {
   Results results_;
   /// LQR subproblem solver
   std::unique_ptr<gar::RiccatiSolverBase<Scalar>> linearSolver_;
-  Filter filter_;
+  FilterTpl<Scalar> filter_;
   /// Linesearch function
-  LinesearchType linesearch_;
+  LinesearchVariant linesearch_;
 
 private:
   /// Callbacks
@@ -167,6 +210,8 @@ template <typename _Scalar> struct SolverProxDDPTpl {
   SolverProxDDPTpl(const Scalar tol = 1e-6, const Scalar mu_init = 0.01,
                    const std::size_t max_iters = 1000,
                    VerboseLevel verbose = VerboseLevel::QUIET,
+                   StepAcceptanceStrategy sa_strategy =
+                       StepAcceptanceStrategy::LINESEARCH_NONMONOTONE,
                    HessianApprox hess_approx = HessianApprox::GAUSS_NEWTON);
 
   inline std::size_t getNumThreads() const { return num_threads_; }
diff --git a/include/aligator/solvers/proxddp/solver-proxddp.hxx b/include/aligator/solvers/proxddp/solver-proxddp.hxx
index 512df57cd..4191b2043 100644
--- a/include/aligator/solvers/proxddp/solver-proxddp.hxx
+++ b/include/aligator/solvers/proxddp/solver-proxddp.hxx
@@ -71,12 +71,13 @@ SolverProxDDPTpl<Scalar>::SolverProxDDPTpl(const Scalar tol,
                                            const Scalar mu_init,
                                            const std::size_t max_iters,
                                            VerboseLevel verbose,
+                                           StepAcceptanceStrategy sa_strategy,
                                            HessianApprox hess_approx)
     : target_tol_(tol), target_dual_tol_(tol), sync_dual_tol(true),
       mu_init(mu_init), verbose_(verbose), hess_approx_(hess_approx),
-      max_iters(max_iters), rollout_max_iters(1),
+      sa_strategy_(sa_strategy), max_iters(max_iters), rollout_max_iters(1),
       filter_(0.0, ls_params.alpha_min, ls_params.max_num_steps),
-      linesearch_(ls_params) {
+      linesearch_() {
   ls_params.interp_type = proxsuite::nlp::LSInterpolation::CUBIC;
 }
 
@@ -146,11 +147,12 @@ void SolverProxDDPTpl<Scalar>::setup(const Problem &problem) {
   if (!problem.checkIntegrity())
     ALIGATOR_RUNTIME_ERROR("Problem failed integrity check.");
 
+  linesearch_.init(sa_strategy_, ls_params);
+
   results_.~Results();
   workspace_.~Workspace();
   new (&results_) Results(problem);
   new (&workspace_) Workspace(problem);
-  linesearch_.setOptions(ls_params);
 
   switch (linear_solver_choice) {
   case LQSolverChoice::SERIAL: {
@@ -512,6 +514,7 @@ bool SolverProxDDPTpl<Scalar>::run(const Problem &problem,
       al_iter++;
       break;
     }
+    linesearch_.reset();
 
     // accept primal updates
     workspace_.prev_xs = results_.xs;
@@ -670,8 +673,10 @@ bool SolverProxDDPTpl<Scalar>::innerLoop(const Problem &problem) {
     Scalar alpha_opt = 1;
     Scalar phi_new;
 
-    switch (sa_strategy) {
-    case StepAcceptanceStrategy::LINESEARCH:
+    switch (sa_strategy_) {
+    case StepAcceptanceStrategy::LINESEARCH_ARMIJO:
+    case StepAcceptanceStrategy::LINESEARCH_NONMONOTONE:
+      assert(linesearch_.isValid());
       phi_new = linesearch_.run(merit_eval_fun, phi0, dphi0, alpha_opt);
       break;
     case StepAcceptanceStrategy::FILTER:
diff --git a/pixi.lock b/pixi.lock
index 3a3e30bbd..668103210 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -41,7 +41,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/exceptiongroup-1.2.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/executing-2.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/fmt-11.0.2-h434a139_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py312h178313f_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.55.0-py312h178313f_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/freetype-2.12.1-h267a509_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gcc-13.3.0-h9576a4e_1.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/gcc_impl_linux-64-13.3.0-hfea6d02_1.conda
@@ -132,7 +132,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libwebp-base-1.4.0-hd590300_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxcb-1.17.0-h8a09558_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libxcrypt-4.4.36-hd590300_1.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.13.4-hb346dea_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.13.5-hb346dea_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/libzlib-1.3.1-hb9d3cd8_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/lz4-c-1.9.4-hcb278e6_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/lzo-2.10-hd590300_1001.conda
@@ -185,7 +185,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/simde-0.8.2-h84d6215_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/six-1.16.0-pyh6c4a22f_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/stack_data-0.6.2-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/suitesparse-7.8.3-hb42a789_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/suitesparse-7.8.3-hb42a789_1.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/sysroot_linux-64-2.17-h4a8ded7_18.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/tbb-2022.0.0-hceb3a55_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/tinyxml2-10.0.0-h59595ed_0.conda
@@ -208,7 +208,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xorg-libxdmcp-1.1.5-hb9d3cd8_0.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/xz-5.2.6-h166bdaf_0.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/yaml-0.2.5-h7f98852_2.tar.bz2
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_6.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_7.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/zlib-1.3.1-hb9d3cd8_2.conda
       - conda: https://conda.anaconda.org/conda-forge/linux-64/zstd-1.5.6-ha6fb4c9_0.conda
       osx-64:
@@ -252,7 +252,7 @@ environments:
       - conda: https://conda.anaconda.org/conda-forge/noarch/exceptiongroup-1.2.2-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/executing-2.1.0-pyhd8ed1ab_0.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-64/fmt-11.0.2-h3c5361c_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/osx-64/fonttools-4.54.1-py312hbe3f5e4_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-64/fonttools-4.55.0-py312h3520af0_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py312h178313f_1.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/fonttools-4.54.1-py312hbe3f5e4_1.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-64/gettext-0.22.5-hdfe23c8_3.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/libxml2-2.13.4-h12808cf_2.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/zeromq-4.3.5-he4ceba3_6.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-64/zstd-1.5.6-h915ae27_0.conda
       osx-arm64:
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       - conda: https://conda.anaconda.org/conda-forge/noarch/executing-2.1.0-pyhd8ed1ab_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.54.1-py312ha0ccf2a_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.55.0-py312h998013c_0.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/freetype-2.12.1-hadb7bae_2.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/gettext-tools-0.22.5-h8414b35_3.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.4-h8424949_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.5-hbbdcc80_0.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/libzlib-1.3.1-h8359307_2.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-h9f5b81c_6.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-hc1bb282_7.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zlib-1.3.1-h8359307_2.conda
       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zstd-1.5.6-hb46c0d2_0.conda
   lint:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py312h178313f_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.55.0-py312h178313f_0.conda
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@@ -3261,7 +3261,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.13.4-hb346dea_2.conda
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@@ -3341,7 +3341,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_6.conda
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       osx-64:
@@ -3387,7 +3387,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/fonttools-4.54.1-py312hbe3f5e4_1.conda
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@@ -3456,7 +3456,7 @@ environments:
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@@ -3535,7 +3535,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/zeromq-4.3.5-he4ceba3_6.conda
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       osx-arm64:
@@ -3581,7 +3581,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.54.1-py312ha0ccf2a_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.55.0-py312h998013c_0.conda
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@@ -3650,7 +3650,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.4-h8424949_2.conda
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@@ -3730,7 +3730,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-h9f5b81c_6.conda
+      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-hc1bb282_7.conda
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       - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zstd-1.5.6-hb46c0d2_0.conda
   openmp:
@@ -3772,7 +3772,7 @@ environments:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-64/zeromq-4.3.5-he4ceba3_6.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.54.1-py312ha0ccf2a_1.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.4-h8424949_2.conda
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-h9f5b81c_6.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py312h178313f_1.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_6.conda
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       osx-arm64:
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-      - conda: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-h9f5b81c_6.conda
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   py39:
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py39h9399b63_1.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_6.conda
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+  url: https://conda.anaconda.org/conda-forge/osx-64/fonttools-4.55.0-py39hd18e689_0.conda
+  sha256: 5d2a4322c9c20b97f7ae532036737a0e1fd8cca54896d9c16fe2519cbb39b1be
+  md5: 66008e96883e821ea1364e980b2bde1a
   depends:
-  - __osx >=11.0
+  - __osx >=10.13
   - brotli
   - munkres
   - python >=3.9,<3.10.0a0
-  - python >=3.9,<3.10.0a0 *_cpython
   - python_abi 3.9.* *_cp39
   - unicodedata2 >=15.1.0
   license: MIT
   license_family: MIT
-  size: 2219590
-  timestamp: 1729530690457
+  size: 2246534
+  timestamp: 1731643634168
 - kind: conda
   name: fonttools
-  version: 4.54.1
-  build: py39h9399b63_1
-  build_number: 1
-  subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/fonttools-4.54.1-py39h9399b63_1.conda
-  sha256: 4f1afc6b458cfd043d3ed22151f4127aab395ff8ad06d44f0e7e7813e6e285bb
-  md5: 1a4772f78ffa4675c84a4219db3934fd
+  version: 4.55.0
+  build: py39hefdd603_0
+  subdir: osx-arm64
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/fonttools-4.55.0-py39hefdd603_0.conda
+  sha256: dffc5e81f0b55ba5e3edfd0598953499b7f2b9fc36d225c0b5e94d228c58bd63
+  md5: 1d4e2d4e0e6eacd407abad673480e8e9
   depends:
-  - __glibc >=2.17,<3.0.a0
+  - __osx >=11.0
   - brotli
-  - libgcc >=13
   - munkres
   - python >=3.9,<3.10.0a0
+  - python >=3.9,<3.10.0a0 *_cpython
   - python_abi 3.9.* *_cp39
   - unicodedata2 >=15.1.0
   license: MIT
   license_family: MIT
-  size: 2322932
-  timestamp: 1729530575488
+  size: 2237078
+  timestamp: 1731643756889
 - kind: conda
   name: freetype
   version: 2.12.1
@@ -12460,13 +12454,12 @@ packages:
   timestamp: 1702724383534
 - kind: conda
   name: libxml2
-  version: 2.13.4
-  build: h12808cf_2
-  build_number: 2
+  version: 2.13.5
+  build: h495214b_0
   subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/libxml2-2.13.4-h12808cf_2.conda
-  sha256: ce806e0f7430b709145ac406e7aacf3833adbdb91e085ed3f4dc8e78cf07038c
-  md5: 0649b977d9e3d2fd579148643884535e
+  url: https://conda.anaconda.org/conda-forge/osx-64/libxml2-2.13.5-h495214b_0.conda
+  sha256: 66e1bf40699daf83b39e1281f06c64cf83499de3a9c05d59477fadded6d85b18
+  md5: 8711bc6fb054192dc432741dcd233ac3
   depends:
   - __osx >=10.13
   - icu >=75.1,<76.0a0
@@ -12475,47 +12468,45 @@ packages:
   - xz >=5.2.6,<6.0a0
   license: MIT
   license_family: MIT
-  size: 601997
-  timestamp: 1730355958301
+  size: 608931
+  timestamp: 1731489767386
 - kind: conda
   name: libxml2
-  version: 2.13.4
-  build: h8424949_2
-  build_number: 2
-  subdir: osx-arm64
-  url: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.4-h8424949_2.conda
-  sha256: 51048cd9d4d7ab3ab440bac01d1db8193ae1bd3e9502cdf6792a69c792fec2e5
-  md5: 3f0764c38bc02720231d49d6035531f2
+  version: 2.13.5
+  build: hb346dea_0
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.13.5-hb346dea_0.conda
+  sha256: 8c9d6a3a421ac5bf965af495d1b0a08c6fb2245ba156550bc064a7b4f8fc7bd8
+  md5: c81a9f1118541aaa418ccb22190c817e
   depends:
-  - __osx >=11.0
+  - __glibc >=2.17,<3.0.a0
   - icu >=75.1,<76.0a0
+  - libgcc >=13
   - libiconv >=1.17,<2.0a0
   - libzlib >=1.3.1,<2.0a0
   - xz >=5.2.6,<6.0a0
   license: MIT
   license_family: MIT
-  size: 572400
-  timestamp: 1730356085177
+  size: 689626
+  timestamp: 1731489608971
 - kind: conda
   name: libxml2
-  version: 2.13.4
-  build: hb346dea_2
-  build_number: 2
-  subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/libxml2-2.13.4-hb346dea_2.conda
-  sha256: a111cb7f2deb6e20ebb475e8426ce5291451476f55f0dec6c220aa51e5a5784f
-  md5: 69b90b70c434b916abf5a1d5ee5d55fb
+  version: 2.13.5
+  build: hbbdcc80_0
+  subdir: osx-arm64
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/libxml2-2.13.5-hbbdcc80_0.conda
+  sha256: 936de9c0e91cb6f178c48ea14313cf6c79bdb1f474c785c117c41492b0407a98
+  md5: 967d4a9dadd710415ee008d862a07c99
   depends:
-  - __glibc >=2.17,<3.0.a0
+  - __osx >=11.0
   - icu >=75.1,<76.0a0
-  - libgcc >=13
   - libiconv >=1.17,<2.0a0
   - libzlib >=1.3.1,<2.0a0
   - xz >=5.2.6,<6.0a0
   license: MIT
   license_family: MIT
-  size: 690019
-  timestamp: 1730355770718
+  size: 583082
+  timestamp: 1731489765442
 - kind: conda
   name: libzlib
   version: 1.3.1
@@ -15639,73 +15630,79 @@ packages:
 - kind: conda
   name: suitesparse
   version: 7.8.3
-  build: h51aacc0_0
-  subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/suitesparse-7.8.3-h51aacc0_0.conda
-  sha256: 1cf6c61eca7577b3044321092021de69c81cdc179f10efd207e0e4cd35fc279f
-  md5: 6cf9b5565082a6c987d9eff694ae9254
+  build: h12cb078_1
+  build_number: 1
+  subdir: osx-arm64
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/suitesparse-7.8.3-h12cb078_1.conda
+  sha256: 495d32b7370a5772cc6e4e71f1d86f5616d6957af8e0ac386f5654b5abfc11ac
+  md5: 25a13d1e2e16bcdf1e5b6b4885cc6da6
   depends:
-  - __osx >=10.13
+  - __osx >=11.0
   - gmp >=6.3.0,<7.0a0
   - libblas >=3.9.0,<4.0a0
   - libcblas >=3.9.0,<4.0a0
-  - libcxx >=17
+  - libcxx >=18
   - libgfortran 5.*
   - libgfortran5 >=13.2.0
   - liblapack >=3.9.0,<4.0a0
+  - llvm-openmp >=18.1.8
   - metis >=5.1.0,<5.1.1.0a0
   - mpfr >=4.2.1,<5.0a0
   - tbb >=2021.13.0
   license: LGPL-2.1-or-later AND BSD-3-Clause AND GPL-2.0-or-later AND Apache-2.0
-  size: 1907384
-  timestamp: 1730383477915
+  size: 1363524
+  timestamp: 1731612132482
 - kind: conda
   name: suitesparse
   version: 7.8.3
-  build: hb42a789_0
-  subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/suitesparse-7.8.3-hb42a789_0.conda
-  sha256: c89f67e032e39dea769c1ebf7383641b776aee2ab42878fbf5745fa300576cb1
-  md5: 216922e19843f5662a2b260f905640cb
+  build: h440b1d8_1
+  build_number: 1
+  subdir: osx-64
+  url: https://conda.anaconda.org/conda-forge/osx-64/suitesparse-7.8.3-h440b1d8_1.conda
+  sha256: c3be1bbc91c783ad97458922bad9949b620ccdbae96e7f947039d7eb5d30bdf8
+  md5: 0a53159c1cb6716733dbf7af55f51308
   depends:
-  - __glibc >=2.17,<3.0.a0
+  - __osx >=10.13
   - gmp >=6.3.0,<7.0a0
   - libblas >=3.9.0,<4.0a0
   - libcblas >=3.9.0,<4.0a0
-  - libgcc >=13
-  - libgfortran
-  - libgfortran5 >=13.3.0
+  - libcxx >=18
+  - libgfortran 5.*
+  - libgfortran5 >=13.2.0
   - liblapack >=3.9.0,<4.0a0
-  - libstdcxx >=13
+  - llvm-openmp >=18.1.8
   - metis >=5.1.0,<5.1.1.0a0
   - mpfr >=4.2.1,<5.0a0
   - tbb >=2021.13.0
   license: LGPL-2.1-or-later AND BSD-3-Clause AND GPL-2.0-or-later AND Apache-2.0
-  size: 1838665
-  timestamp: 1730383035378
+  size: 1919414
+  timestamp: 1731612041377
 - kind: conda
   name: suitesparse
   version: 7.8.3
-  build: hcefb574_0
-  subdir: osx-arm64
-  url: https://conda.anaconda.org/conda-forge/osx-arm64/suitesparse-7.8.3-hcefb574_0.conda
-  sha256: d4459ec19fd92676e3fe2a53636c6f26ea56593d2a2266d72f0ad0505f8c7718
-  md5: 4cbbd1ae8e2e74f2480de640c12941a2
+  build: hb42a789_1
+  build_number: 1
+  subdir: linux-64
+  url: https://conda.anaconda.org/conda-forge/linux-64/suitesparse-7.8.3-hb42a789_1.conda
+  sha256: dff3ad8d66a4050763b1b63f4cab7c9b5f2e0e93d71639aebd8814b5ab23a9b4
+  md5: 216fa6eae33d712fa688fa2d113a65ad
   depends:
-  - __osx >=11.0
+  - __glibc >=2.17,<3.0.a0
+  - _openmp_mutex >=4.5
   - gmp >=6.3.0,<7.0a0
   - libblas >=3.9.0,<4.0a0
   - libcblas >=3.9.0,<4.0a0
-  - libcxx >=17
-  - libgfortran 5.*
-  - libgfortran5 >=13.2.0
+  - libgcc >=13
+  - libgfortran
+  - libgfortran5 >=13.3.0
   - liblapack >=3.9.0,<4.0a0
+  - libstdcxx >=13
   - metis >=5.1.0,<5.1.1.0a0
   - mpfr >=4.2.1,<5.0a0
   - tbb >=2021.13.0
   license: LGPL-2.1-or-later AND BSD-3-Clause AND GPL-2.0-or-later AND Apache-2.0
-  size: 1355028
-  timestamp: 1730383410695
+  size: 1840784
+  timestamp: 1731611614601
 - kind: conda
   name: sysroot_linux-64
   version: '2.17'
@@ -16664,12 +16661,12 @@ packages:
 - kind: conda
   name: zeromq
   version: 4.3.5
-  build: h3b0a872_6
-  build_number: 6
+  build: h3b0a872_7
+  build_number: 7
   subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_6.conda
-  sha256: e67288b1c98a31ee58a5c07bdd873dbe08e75f752e1ad605d5e8c0697339903e
-  md5: 113506c8d2d558e733f5c38f6bf08c50
+  url: https://conda.anaconda.org/conda-forge/linux-64/zeromq-4.3.5-h3b0a872_7.conda
+  sha256: a4dc72c96848f764bb5a5176aa93dd1e9b9e52804137b99daeebba277b31ea10
+  md5: 3947a35e916fcc6b9825449affbf4214
   depends:
   - __glibc >=2.17,<3.0.a0
   - krb5 >=1.21.3,<1.22.0a0
@@ -16678,44 +16675,44 @@ packages:
   - libstdcxx >=13
   license: MPL-2.0
   license_family: MOZILLA
-  size: 335528
-  timestamp: 1728364029042
+  size: 335400
+  timestamp: 1731585026517
 - kind: conda
   name: zeromq
   version: 4.3.5
-  build: h9f5b81c_6
-  build_number: 6
-  subdir: osx-arm64
-  url: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-h9f5b81c_6.conda
-  sha256: 5c5061c976141eccbbb2aec21483ddd10fd1df4fd9bcf638e3fd57b2bd85721f
-  md5: 84121ef1717cdfbecedeae70142706cc
+  build: h7130eaa_7
+  build_number: 7
+  subdir: osx-64
+  url: https://conda.anaconda.org/conda-forge/osx-64/zeromq-4.3.5-h7130eaa_7.conda
+  sha256: b932dce8c9de9a8ffbf0db0365d29677636e599f7763ca51e554c43a0c5f8389
+  md5: 6a0a76cd2b3d575e1b7aaeb283b9c3ed
   depends:
-  - __osx >=11.0
+  - __osx >=10.13
   - krb5 >=1.21.3,<1.22.0a0
-  - libcxx >=17
+  - libcxx >=18
   - libsodium >=1.0.20,<1.0.21.0a0
   license: MPL-2.0
   license_family: MOZILLA
-  size: 280870
-  timestamp: 1728363954972
+  size: 292112
+  timestamp: 1731585246902
 - kind: conda
   name: zeromq
   version: 4.3.5
-  build: he4ceba3_6
-  build_number: 6
-  subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/zeromq-4.3.5-he4ceba3_6.conda
-  sha256: 0e2a6ced111fd99b66b76ec797804ab798ec190a88a2779060f7a8787c343ee0
-  md5: 00ec9f2a5e21bbbd22ffbbc12b3df286
+  build: hc1bb282_7
+  build_number: 7
+  subdir: osx-arm64
+  url: https://conda.anaconda.org/conda-forge/osx-arm64/zeromq-4.3.5-hc1bb282_7.conda
+  sha256: 9e585569fe2e7d3bea71972cd4b9f06b1a7ab8fa7c5139f92a31cbceecf25a8a
+  md5: f7e6b65943cb73bce0143737fded08f1
   depends:
-  - __osx >=10.13
+  - __osx >=11.0
   - krb5 >=1.21.3,<1.22.0a0
-  - libcxx >=17
+  - libcxx >=18
   - libsodium >=1.0.20,<1.0.21.0a0
   license: MPL-2.0
   license_family: MOZILLA
-  size: 290634
-  timestamp: 1728364170966
+  size: 281565
+  timestamp: 1731585108039
 - kind: conda
   name: zipp
   version: 3.21.0
diff --git a/pixi.toml b/pixi.toml
index 1350c02f5..ca4af5758 100644
--- a/pixi.toml
+++ b/pixi.toml
@@ -20,7 +20,7 @@ libboost-python-devel = ">=1.80.0"
 eigen = ">=3.4.0"
 python = ">=3.9.0"
 eigenpy = ">=3.8.0,!=3.10.0"
-proxsuite-nlp = ">=0.8.0"
+proxsuite-nlp = ">=0.10.0"
 fmt = ">=10.0.0"
 benchmark = ">=1.8.0"
 pytest = ">=8.3.0"
diff --git a/src/core/history-callback.cpp b/src/core/history-callback.cpp
index ddccaccb0..301ed98b2 100644
--- a/src/core/history-callback.cpp
+++ b/src/core/history-callback.cpp
@@ -1,4 +1,4 @@
-#include "aligator/helpers/history-callback.hpp"
+#include "aligator/helpers/history-callback.hxx"
 
 namespace aligator {
 
diff --git a/tests/python/test_constrained_dynamics.py b/tests/python/test_constrained_dynamics.py
index c8ca1e745..e93bb9116 100644
--- a/tests/python/test_constrained_dynamics.py
+++ b/tests/python/test_constrained_dynamics.py
@@ -258,9 +258,7 @@ def test_constrained_dynamics():
     tol = 1e-5
     mu_init = 0.01
     verbose = aligator.VerboseLevel.VERBOSE
-    history_cb = aligator.HistoryCallback()
     solver = aligator.SolverProxDDP(tol, mu_init, verbose=verbose, max_iters=200)
-    solver.registerCallback("his", history_cb)
     solver.setup(problem)
     conv = solver.run(problem, xs_init, us_init)
 
diff --git a/tests/python/test_solver.py b/tests/python/test_solver.py
index 32f200d75..d0915b612 100644
--- a/tests/python/test_solver.py
+++ b/tests/python/test_solver.py
@@ -60,7 +60,14 @@ def test_no_node():
     solver.setup(problem)
 
 
-@pytest.mark.parametrize("strategy", [aligator.SA_FILTER, aligator.SA_LINESEARCH])
+@pytest.mark.parametrize(
+    "strategy",
+    [
+        aligator.SA_FILTER,
+        aligator.SA_LINESEARCH_ARMIJO,
+        aligator.SA_LINESEARCH_NONMONOTONE,
+    ],
+)
 def test_proxddp_lqr(strategy):
     nx = 3
     nu = 3