Clarify solver statistics and gradient evaluation details for the LM solver in paper.md

Author: MohamedLaghdafHABIBOULLAH

paper/examples/Project.toml

@@ -6,6 +6,5 @@ PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
 ProximalAlgorithms = "140ffc9f-1907-541a-a177-7475e0a401e9"
 ProximalCore = "dc4f5ac2-75d1-4f31-931e-60435d74994b"
 ProximalOperators = "a725b495-10eb-56fe-b38b-717eba820537"
-RegularizedOptimization = "196f2941-2d58-45ba-9f13-43a2532b2fa8"
 RegularizedProblems = "ea076b23-609f-44d2-bb12-a4ae45328278"
 ShiftedProximalOperators = "d4fd37fa-580c-4e43-9b30-361c21aae263"

paper/paper.md

@@ -169,11 +169,12 @@ solver = LMSolver(reg_nls)                                   # Choose solver
 
 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:
+
+We report the following solver statistics in table: the final value of \(f\) at convergence; the status of convergence of each solver (**Status**); the number of evaluations of the smooth objective ($\# f$); the number of evaluations of the gradient ($\# \nabla f$); the number of proximal operator evaluations ($\# \text{prox}$); the elapsed time $t$ in seconds and the final objective value $(f + h)(x^*)$ (**Objective**).
 
 \input{examples/Benchmark.tex}
 
-* For the LM solver, gradient evaluations count equals the number of Jacobian–vector and adjoint-Jacobian–vector products.
+* For the LM solver, gradient evaluations count $\#\nabla f$ equals the number of Jacobian–vector and adjoint-Jacobian–vector products.
 
 ## Discussion