vipsegm. Numerical solution for pseudomonotone variational inequality problems by extragradient methods.
Manopt. With Manopt, you can solve optimization problems on manifolds using state-of-the-art algorithms, with minimal effort.
SGDLibrary. MATLAB/Octave library for stochastic optimization algorithms.
FOM, is a MATLAB toolbox containing a collection of first order methods for solving (mainly) convex optimization problems.
CVX: Matlab Software for Disciplined Convex Programming.
TFOCS: Templates for First-Order Conic Solvers. Introduction
NESTA: Nesterov's Algorithm. A Fast and Accurate First-order Method for Sparse Recovery.
UNLocBoX: Matlab convex optimization toolbox.
YALMIP: MATLAB toolbox for optimization modeling.
PN2O: Parallel Algorithms and Numerical Nonlinear Optimization,
l1benchmark: Fast \(\ell_1\) Minimization Algorithms.
FASTA. Fast Adaptive Shrinkage/Thresholding Algorithm.
Toolbox Sparse Optmization: Optimization codes for sparsity related signal processing.