Refine descriptions in the model-based framework section of paper.md for clarity and consistency

Author: MohamedLaghdafHABIBOULLAH

paper/paper.md

@@ -65,7 +65,7 @@ While [ProximalOperators.jl](https://github.com/JuliaFirstOrder/ProximalOperator
 ## Model-based framework for nonsmooth methods
 
 In Julia, \eqref{eq:nlp} can be solved using [ProximalAlgorithms.jl](https://github.com/JuliaFirstOrder/ProximalAlgorithms.jl), which implements in-place, first-order, line-search–based methods [@stella-themelis-sopasakis-patrinos-2017;@themelis-stella-patrinos-2017].
-Most of these methods are splitting schemes that either alternate between the proximal operators of $f$ and $h$, as in the **Douglas–Rachford** solver [@eckstein1992douglas], or take a step along a direction $d$, which depends on the gradient of $f$, possibly modified by a Quasi-Newton approximation (e.g., L-BFGS)—followed by proximal steps on the nonsmooth part $h$. In some cases, such as with the **PANOC** [@stella-themelis-sopasakis-patrinos-2017] solver, this process is augmented with a line-search mechanism along $d$.
+Most of these methods are splitting schemes that either alternate between the proximal operators of $f$ and $h$, as in the **Douglas–Rachford** solver [@eckstein1992douglas], or take a step along a direction $d$, which depends on the gradient of $f$, possibly modified by a L-BFGS Quasi-Newton approximation followed by proximal steps on the nonsmooth part $h$. In some cases, such as with the **PANOC** [@stella-themelis-sopasakis-patrinos-2017] solver, this process is augmented with a line-search mechanism along $d$.
 
 By contrast, [RegularizedOptimization.jl](https://github.com/JuliaSmoothOptimizers/RegularizedOptimization.jl) focuses on model-based approaches such as trust-region and quadratic regularization algorithms.
 As shown in [@aravkin-baraldi-orban-2022], model-based methods typically require fewer evaluations of the objective and its gradient than first-order line search methods, at the expense of requiring a lot of proximal iterations to solve the subproblems.
@@ -119,7 +119,6 @@ This design makes for a convenient source of reproducible problem instances for
 
 The package includes a comprehensive suite of unit tests that cover all functionalities, ensuring reliability and correctness.
 Extensive documentation is provided, including a user guide, API reference, and examples to help users get started quickly.
-Aqua.jl is used to test the package dependencies.
 Documentation is built using Documenter.jl.
 
 ## Application studies
@@ -168,7 +167,7 @@ solver = LMSolver(reg_nls)                                   # Choose solver
 
 ## Numerical results
 
-We compare **PANOC** [@stella-themelis-sopasakis-patrinos-2017](from [ProximalAlgorithms.jl](https://github.com/JuliaFirstOrder/ProximalAlgorithms.jl)) against **TR**, **R2N**, and **LM** from our library.
+We compare **PANOC** [@stella-themelis-sopasakis-patrinos-2017] (from [ProximalAlgorithms.jl](https://github.com/JuliaFirstOrder/ProximalAlgorithms.jl)) against **TR**, **R2N**, and **LM** from our library.
 In order to do so, we implemented a wrapper for **PANOC** to make it compatible with our problem definition.
 The results are summarized in the combined table below: