rename "algorithms" as "solvers"

Author: MaxenceGollier

docs/src/algorithms.md

@@ -1,7 +1,7 @@
-# [Algorithms](@id algorithms)
+# [Solvers](@id algorithms)
 
 ## General case
-The algorithms in this package are based upon the approach of [aravkin-baraldi-orban-2022](@cite).
+The solvers in this package are based upon the approach of [aravkin-baraldi-orban-2022](@cite).
 Suppose we are given the general regularized problem
 ```math
 \underset{x \in \mathbb{R}^n}{\text{minimize}} \quad f(x) + h(x),
@@ -25,18 +25,18 @@ or a quadratic regularization
 ```math
 s_0 \in \underset{s \in \mathbb{R}^n}{\argmin} \  \varphi(s; x_0) + \psi(s; x_0) + \tfrac{1}{2} \sigma \|s\|^2_2.
 ```
-Algorithms that work with a trust-region are [`TR`](@ref TR) and [`TRDH`](@ref TRDH) and the ones working with a quadratic regularization are [`R2`](@ref R2), [`R2N`](@ref R2N) and [`R2DH`](@ref R2DH)
+Solvers that work with a trust-region are [`TR`](@ref TR) and [`TRDH`](@ref TRDH) and the ones working with a quadratic regularization are [`R2`](@ref R2), [`R2N`](@ref R2N) and [`R2DH`](@ref R2DH)
 
 The models for the smooth part `f` in this package are always quadratic models of the form
 ```math
 \varphi(s; x_0) = f(x_0) + \nabla f(x_0)^T s + \tfrac{1}{2} s^T H(x_0) s,
 ```
 where $H(x_0)$ is a symmetric matrix that can be either $0$, the Hessian of $f$ (if it exists) or a quasi-Newton approximation.
-Some algorithms require a specific structure for $H$, for an overview, refer to the table below.
+Some solvers require a specific structure for $H$, for an overview, refer to the table below.
 
-The following table gives an overview of the available algorithms in the general case.
+The following table gives an overview of the available solvers in the general case.
 
-Algorithm | Quadratic Regularization | Trust Region | Quadratic term for $\varphi$ : H | Reference
+Solver | Quadratic Regularization | Trust Region | Quadratic term for $\varphi$ : H | Reference
 ----------|--------------------------|--------------|---------------|----------
 [`R2`](@ref R2) | Yes | No | $H = 0$  | [aravkin-baraldi-orban-2022; Algorithm 6.1](@cite)
 [`R2N`](@ref R2N) | Yes | No | Any Symmetric| [diouane-habiboullah-orban-2024; Algorithm 1](@cite)
@@ -45,7 +45,7 @@ Algorithm | Quadratic Regularization | Trust Region | Quadratic term for $\varph
 [`TRDH`](@ref TRDH) | No | Yes | Any Diagonal | [leconte-orban-2025; Algorithm 5.1](@cite)
 
 ## Nonlinear least-squares
-This package provides two algorithms, [`LM`](@ref LM) and [`LMTR`](@ref LMTR), specialized for regularized, nonlinear least-squares, i.e., problems of the form
+This package provides two solvers, [`LM`](@ref LM) and [`LMTR`](@ref LMTR), specialized for regularized, nonlinear least-squares, i.e., problems of the form
 ```math
 \underset{x \in \mathbb{R}^n}{\text{minimize}} \quad \tfrac{1}{2}\|F(x)\|_2^2 + h(x),
 ```
@@ -55,8 +55,8 @@ In that case, the model $\varphi$ is defined as
 \varphi(s; x) = \tfrac{1}{2}\|F(x) + J(x)s\|_2^2,
 ```
 where $J(x)$ is the Jacobian of $F$ at $x$.
-Similar to the algorithms in the previous section, we either add a quadratic regularization to the model ([`LM`](@ref LM)) or a trust-region ([`LMTR`](@ref LMTR)).
-These algorithms are described in [aravkin-baraldi-orban-2024](@cite).
+Similar to the solvers in the previous section, we either add a quadratic regularization to the model ([`LM`](@ref LM)) or a trust-region ([`LMTR`](@ref LMTR)).
+These solvers are described in [aravkin-baraldi-orban-2024](@cite).
 
 ## Constrained Optimization
 For constrained, regularized optimization,

docs/src/examples/basic.md

@@ -43,7 +43,7 @@ regularized_pb = RegularizedNLPModel(f_model, h)
 ```
 
 ## Solving the problem
-We can now choose one of the algorithms presented [here](@ref algorithms) to solve the problem we defined above.
+We can now choose one of the solvers presented [here](@ref algorithms) to solve the problem we defined above.
 Please refer to other sections of this documentation to make the wisest choice for your particular problem.
 Depending on the problem structure and on requirements from the user, some solvers are more appropriate than others.
 The following tries to give a quick overview of what choices one can make.
@@ -70,7 +70,7 @@ println("R2 converged after $(out.iter) iterations to the solution x = $(out.sol
 println("--------------------------------------------------------------------------------------")
 
 # Now, on this example, we can actually use second information on f. 
-# To do so, we are going to use TR, a trust-region algorithm that can exploit second order information.
+# To do so, we are going to use TR, a trust-region solver that can exploit second order information.
 out = TR(regularized_pb, verbose = 10, atol = 1e-3)
 println("TR converged after $(out.iter) iterations to the solution x = $(out.solution)")
 println("--------------------------------------------------------------------------------------")

docs/src/examples/ls.md

@@ -50,7 +50,7 @@ regularized_pb = RegularizedNLPModel(f_model, h)
 ```
 
 ## Solving the problem
-We can now choose one of the algorithms presented [here](@ref algorithms) to solve the problem we defined above.
+We can now choose one of the solvers presented [here](@ref algorithms) to solve the problem we defined above.
 In the case of least-squares, it is usually more appropriate to choose LM or LMTR.
 ```@example
 using LLSModels