UNLocBoX: A MATLAB convex optimization toolbox for proximal-splitting methods

Abstract: Convex optimization is an essential tool for machine learning, as many of its problems can be formulated as minimization problems of specific objective functions. While there is a large variety of algorithms available to solve convex problems, we can argue that it becomes more and more important to focus on efficient, scalable methods that can deal with big data. When the objective function can be written as a sum of "simple" terms, proximal splitting methods are a good choice. UNLocBoX is a MATLAB library that implements many of these methods, designed to solve convex optimization problems of the form $\min_{x \in \mathbb{R}^N} \sum_{n=1}^K f_n(x).$ It contains the most recent solvers such as FISTA, Douglas-Rachford, SDMM as well a primal dual techniques such as Chambolle-Pock and forward-backward-forward. It also includes an extensive list of common proximal operators that can be combined, allowing for a quick implementation of a large variety of convex problems.