Finding sparse solutions to problems with convex constraints via concave programming

Abstract

In this work, we consider a class of nonlinear optimization problems with convex constraints with the aim of computing sparse solutions. This is an important task arising in various fields such as machine learning, signal processing, data analysis. We adopt a concave optimization-based approach, we define an effective version of the Frank-Wolfe algorithm, and we prove the global convergence of the method. Finally, we report numerical results on test problems showing both the effectiveness of the concave approach and the efficiency of the implemented algorithm.