remove panoc comparison

Author: MohamedLaghdafHABIBOULLAH

paper/examples/Benchmark.tex

@@ -1,10 +1,8 @@
 \begin{tabular}{lcrrrrr}
   \hline
   \textbf{Method} & \textbf{Status} & \textbf{$t$($s$)} & \textbf{$\#f$} & \textbf{$\#\nabla f$} & \textbf{$\#prox$} & \textbf{Objective} \\\hline
-  PANOC (SVM) & first\_order & 39.7779 & 3713 & 3713 & 2269 & 188.924 \\
   TR (LSR1, SVM) & first\_order & 4.0193 & 347 & 291 & 4037 & 179.837 \\
   R2N (LSR1, SVM) & first\_order & 2.5033 & 185 & 101 & 27932 & 192.493 \\
-  PANOC (NNMF) & first\_order & 0.0258 & 437 & 437 & 238 & 143.546 \\
   TR (LBFGS, NNMF) & first\_order & 0.1089 & 42 & 40 & 3160 & 976.06 \\
   R2N (LBFGS, NNMF) & first\_order & 0.4921 & 169 & 107 & 17789 & 411.727 \\
   LM (NNMF) & first\_order & 0.4542 & 15 & 27723 & 12320 & 131.183 \\\hline

paper/paper.md

@@ -167,8 +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.
-In order to do so, we implemented a wrapper for **PANOC** to make it compatible with our problem definition.
+We compare **TR**, **R2N**, and **LM** from our library.
 
 We report the following solver statistics in the table: the convergence status of each solver, the number of evaluations of $f$, the number of evaluations of $\nabla f$, the number of proximal operator evaluations, the elapsed time in seconds and the final objective value.
 On the SVM and NNMF problems, we use limited-memory SR1 and BFGS Hessian approximations, respectively.
@@ -181,8 +180,9 @@ The subproblem solver is **R2**.
 All methods successfully reduced the optimality measure below the specified tolerance of $10^{-4}$, and thus converged to an approximate first-order stationary point.
 However, the final objective values differ due to the nonconvexity of the problems.
 
-- **SVM with $\ell^{1/2}$ penalty:** **TR** and **R2N** require far fewer function and gradient evaluations than **PANOC**, at the expense of more proximal iterations. Since each proximal step is inexpensive, **TR** and **R2N** are much faster overall.  
-- **NNMF with constrained $\ell_0$ penalty:** **PANOC** is the fastest, even though it requires a larger number of function and gradient evaluations than **TR** and **R2N**. **LM** is competitive in terms of function calls but incurs many Jacobian–vector products; it nevertheless achieves the lowest objective value.
+- **SVM with $\ell^{1/2}$ penalty:** **R2N** is the fastest, requiring the fewest function and gradient evaluations compared to **TR**.
+However, it requires more proximal evaluations, but these are inexpensive.
+- **NNMF with constrained $\ell_0$ penalty:** **TR** is the fastest, and requires a fewer number of function and gradient evaluations than **R2N**. **LM** is competitive in terms of function calls but incurs many Jacobian–vector products; it nevertheless achieves the lowest objective value.
 
 Additional tests (e.g., other regularizers, constraint types, and scaling dimensions) have also been conducted, and a full benchmarking campaign is currently underway.