Add monotonicity parameter to LMSolver and TRSolver with history tracking

Author: MohamedLaghdafHABIBOULLAH

src/LM_alg.jl

@@ -22,14 +22,15 @@ mutable struct LMSolver{
   has_bnds::Bool
   l_bound::V
   u_bound::V
+  m_fh_hist::V
   l_bound_m_x::V
   u_bound_m_x::V
   subsolver::ST
   subpb::PB
   substats::GenericExecutionStats{T, V, V, T}
 end
 
-function LMSolver(reg_nls::AbstractRegularizedNLPModel{T, V}; subsolver = R2Solver) where {T, V}
+function LMSolver(reg_nls::AbstractRegularizedNLPModel{T, V}; subsolver = R2Solver, m_monotone::Int = 1) where {T, V}
   x0 = reg_nls.model.meta.x0
   l_bound = reg_nls.model.meta.lvar
   u_bound = reg_nls.model.meta.uvar
@@ -54,6 +55,8 @@ function LMSolver(reg_nls::AbstractRegularizedNLPModel{T, V}; subsolver = R2Solv
     u_bound_m_x = similar(xk, 0)
   end
 
+  m_fh_hist = fill(T(-Inf), m_monotone - 1)
+
   ψ =
     has_bnds ? shifted(reg_nls.h, xk, l_bound_m_x, u_bound_m_x, reg_nls.selected) :
     shifted(reg_nls.h, xk)
@@ -80,6 +83,7 @@ function LMSolver(reg_nls::AbstractRegularizedNLPModel{T, V}; subsolver = R2Solv
     u_bound,
     l_bound_m_x,
     u_bound_m_x,
+    m_fh_hist,
     subsolver,
     subpb,
     substats,
@@ -105,7 +109,7 @@ where F(x) and J(x) are the residual and its Jacobian at x, respectively, ψ(s;
 
 For advanced usage, first define a solver "LMSolver" to preallocate the memory used in the algorithm, and then call `solve!`:
 
-    solver = LMSolver(reg_nls; subsolver = R2Solver)
+    solver = LMSolver(reg_nls; subsolver = R2Solver, m_monotone = 1)
     solve!(solver, reg_nls)
 
     stats = RegularizedExecutionStats(reg_nls)
@@ -130,6 +134,7 @@ For advanced usage, first define a solver "LMSolver" to preallocate the memory u
 - `η2::T = T(0.9)`: very successful iteration threshold;
 - `γ::T = T(3)`: regularization parameter multiplier, σ := σ/γ when the iteration is very successful and σ := σγ when the iteration is unsuccessful;
 - `θ::T = 1/(1 + eps(T)^(1 / 5))`: is the model decrease fraction with respect to the decrease of the Cauchy model;
+- `m_monotone::Int = 1`: monotonicity parameter. By default, LM is monotone but the non-monotone variant will be used if `m_monotone > 1`;
 - `subsolver = R2Solver`: the solver used to solve the subproblems.
 
 The algorithm stops either when `√(ξₖ/νₖ) < atol + rtol*√(ξ₀/ν₀) ` or `ξₖ < 0` and `√(-ξₖ/νₖ) < neg_tol` where ξₖ := f(xₖ) + h(xₖ) - φ(sₖ; xₖ) - ψ(sₖ; xₖ), and √(ξₖ/νₖ) is a stationarity measure.
@@ -166,7 +171,8 @@ end
 function LM(reg_nls::AbstractRegularizedNLPModel; kwargs...)
   kwargs_dict = Dict(kwargs...)
   subsolver = pop!(kwargs_dict, :subsolver, R2Solver)
-  solver = LMSolver(reg_nls, subsolver = subsolver)
+  m_monotone = pop!(kwargs_dict, :m_monotone, 1)
+  solver = LMSolver(reg_nlp, subsolver = subsolver, m_monotone = m_monotone)
   stats = RegularizedExecutionStats(reg_nls)
   solve!(solver, reg_nls, stats; kwargs_dict...)
   return stats
@@ -214,7 +220,11 @@ function SolverCore.solve!(
   ψ = solver.ψ
   xkn = solver.xkn
   s = solver.s
+  m_fh_hist = solver.m_fh_hist .= T(-Inf)
   has_bnds = solver.has_bnds
+
+  m_monotone = length(m_fh_hist) + 1
+
   if has_bnds
     l_bound = solver.l_bound
     u_bound = solver.u_bound
@@ -275,6 +285,7 @@ function SolverCore.solve!(
   set_solver_specific!(stats, :smooth_obj, fk)
   set_solver_specific!(stats, :nonsmooth_obj, hk)
   set_solver_specific!(stats, :prox_evals, prox_evals + 1)
+  m_monotone > 1 && (m_fh_hist[stats.iter % (m_monotone - 1) + 1] = fk + hk)
 
   φ1 = let Fk = Fk, ∇fk = ∇fk
     d -> dot(Fk, Fk) / 2 + dot(∇fk, d) # ∇fk = Jk^T Fk
@@ -345,7 +356,8 @@ function SolverCore.solve!(
       error("LM: failed to compute a step: ξ = $ξ")
     end
 
-    Δobj = fk + hk - (fkn + hkn) + max(1, abs(fk + hk)) * 10 * eps()
+    fhmax = m_monotone > 1 ? maximum(m_fh_hist) : fk + hk
+    Δobj = fhmax - (fkn + hkn) + max(1, abs(fk + hk)) * 10 * eps()
     ρk = Δobj / ξ
 
     verbose > 0 &&
@@ -400,6 +412,8 @@ function SolverCore.solve!(
       σk = σk * γ
     end
 
+    m_monotone > 1 && (m_fh_hist[stats.iter % (m_monotone - 1) + 1] = fk + hk)
+
     set_objective!(stats, fk + hk)
     set_solver_specific!(stats, :smooth_obj, fk)
     set_solver_specific!(stats, :nonsmooth_obj, hk)

src/TR_alg.jl

@@ -23,6 +23,7 @@ mutable struct TRSolver{
   u_bound::V
   l_bound_m_x::V
   u_bound_m_x::V
+  m_fh_hist::V
   subsolver::ST
   subpb::PB
   substats::GenericExecutionStats{T, V, V, T}
@@ -32,6 +33,7 @@ function TRSolver(
   reg_nlp::AbstractRegularizedNLPModel{T, V};
   χ::X = NormLinf(one(T)),
   subsolver = R2Solver,
+  m_monotone::Int = 1,
 ) where {T, V, X}
   x0 = reg_nlp.model.meta.x0
   l_bound = reg_nlp.model.meta.lvar
@@ -54,6 +56,8 @@ function TRSolver(
     u_bound_m_x = similar(xk, 0)
   end
 
+  m_fh_hist = fill(T(-Inf), m_monotone - 1)
+
   ψ =
     has_bnds || subsolver == TRDHSolver ?
     shifted(reg_nlp.h, xk, l_bound_m_x, u_bound_m_x, reg_nlp.selected) :
@@ -81,6 +85,7 @@ function TRSolver(
     u_bound,
     l_bound_m_x,
     u_bound_m_x,
+    m_fh_hist,
     subsolver,
     subpb,
     substats,
@@ -107,7 +112,7 @@ where φ(s ; xₖ) = f(xₖ) + ∇f(xₖ)ᵀs + ½ sᵀ Bₖ s  is a quadratic a
 
 For advanced usage, first define a solver "TRSolver" to preallocate the memory used in the algorithm, and then call `solve!`:
 
-    solver = TR(reg_nlp; χ =  NormLinf(1), subsolver = R2Solver)
+    solver = TRSolver(reg_nlp; χ =  NormLinf(1), subsolver = R2Solver, m_monotone = 1)
     solve!(solver, reg_nlp)
 
     stats = RegularizedExecutionStats(reg_nlp)
@@ -129,6 +134,7 @@ For advanced usage, first define a solver "TRSolver" to preallocate the memory u
 - `η1::T = √√eps(T)`: successful iteration threshold;
 - `η2::T = T(0.9)`: very successful iteration threshold;
 - `γ::T = T(3)`: trust-region radius parameter multiplier. Must satisfy `γ > 1`. The trust-region radius is updated as Δ := Δ*γ when the iteration is very successful and Δ := Δ/γ when the iteration is unsuccessful;
+- `m_monotone::Int = 1`: monotonicity parameter. By default, TR is monotone but the non-monotone variant will be used if `m_monotone > 1`;
 - `χ::F =  NormLinf(1)`: norm used to define the trust-region;`
 - `subsolver::S = R2Solver`: subsolver used to solve the subproblem that appears at each iteration.
 - `sub_kwargs::NamedTuple = NamedTuple()`: a named tuple containing the keyword arguments to be sent to the subsolver. The solver will fail if invalid keyword arguments are provided to the subsolver. For example, if the subsolver is `R2Solver`, you can pass `sub_kwargs = (max_iter = 100, σmin = 1e-6,)`.
@@ -175,7 +181,8 @@ function TR(reg_nlp::AbstractRegularizedNLPModel{T, V}; kwargs...) where {T, V}
   kwargs_dict = Dict(kwargs...)
   subsolver = pop!(kwargs_dict, :subsolver, R2Solver)
   χ = pop!(kwargs_dict, :χ, NormLinf(one(T)))
-  solver = TRSolver(reg_nlp, subsolver = subsolver, χ = χ)
+  m_monotone = pop!(kwargs_dict, :m_monotone, 1)
+  solver = TRSolver(reg_nlp, subsolver = subsolver, χ = χ, m_monotone = m_monotone)
   stats = RegularizedExecutionStats(reg_nlp)
   solve!(solver, reg_nlp, stats; kwargs_dict...)
   return stats
@@ -221,8 +228,11 @@ function SolverCore.solve!(
   xkn = solver.xkn
   s = solver.s
   χ = solver.χ
+  m_fh_hist = solver.m_fh_hist .= T(-Inf)
   has_bnds = solver.has_bnds
 
+  m_monotone = length(m_fh_hist) + 1
+
   if has_bnds || isa(solver.subsolver, TRDHSolver) #TODO elsewhere ?
     l_bound_m_x, u_bound_m_x = solver.l_bound_m_x, solver.u_bound_m_x
     l_bound, u_bound = solver.l_bound, solver.u_bound
@@ -293,6 +303,7 @@ function SolverCore.solve!(
   set_solver_specific!(stats, :smooth_obj, fk)
   set_solver_specific!(stats, :nonsmooth_obj, hk)
   set_solver_specific!(stats, :prox_evals, prox_evals + 1)
+  m_monotone > 1 && (m_fh_hist[stats.iter % (m_monotone - 1) + 1] = fk + hk)
 
   # models
   φ1 = let ∇fk = ∇fk
@@ -380,7 +391,8 @@ function SolverCore.solve!(
     hkn = @views h(xkn[selected])
     sNorm = χ(s)
 
-    Δobj = fk + hk - (fkn + hkn) + max(1, abs(fk + hk)) * 10 * eps()
+    fhmax = m_monotone > 1 ? maximum(m_fh_hist) : fk + hk
+    Δobj = fhmax - (fkn + hkn) + max(1, abs(fk + hk)) * 10 * eps()
     ξ = hk - mk(s) + max(1, abs(hk)) * 10 * eps()
 
     if (ξ ≤ 0 || isnan(ξ))
@@ -452,6 +464,8 @@ function SolverCore.solve!(
       end
     end
 
+    m_monotone > 1 && (m_fh_hist[stats.iter % (m_monotone - 1) + 1] = fk + hk)
+
     set_objective!(stats, fk + hk)
     set_solver_specific!(stats, :smooth_obj, fk)
     set_solver_specific!(stats, :nonsmooth_obj, hk)