Support identification in stochastic Frank-Wolfe variants

This thesis is about some variants of the Frank-Wolfe algorithm (FW), one of the earliest existing methods for constrained convex optimization. When dealing with big data, the optimal solutions to this type of problems are usually very sparse and identifying the set of the non zero components becomes a very important task. After reporting some identification results for the away-step variant (AFW), a numerical analysis is conducted for the stochastic away-step FW (ASFW), testing a constrained least squares regression problem. In order to detect such identification property, the algorithms of AFW and ASFW are implemented and compared on a hundred instances of the considered problem. Finally several performance analysis are carried out on different sample sizes used in the stochastic method, leading to encouraging identification results.