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Séminaire ICI : Luis Briceño-Arias

Titre du séminaire et orateur

Splitting algorithms for solving composite convex optimisation problems: a survey and new results.

Luis Briceño-Arias, Universidad Técnica Federico Santa María in Santiago, Chile.

Date et lieu

Mardi 28 mars 2017, 11h.

ENSEA, salle 384.

Abstract

In this talk we provide a survey of convex optimisation algorithms, starting from the classical steepest descent method and proximal point algorithm, in the case of minimising a single convex function, up to complex primal-dual algorithms using the proximity operator, in the case when the objective function can be decomposed in sums of convex functions and compositions with linear operators. The importance of the optimization problems under study are justified via some examples.

We explore connections between the methods and first order optimality conditions of the associated optimisation problems, and we study the convergence of the algorithms vía properties of specific non expansive operators, whose fixed points are their solutions.

Finally, we explore new algorithms and variants, in particular, connections of some known primal-dual schemes with the proximal point algorithm.

Bio

Luis Briceño-Arias is an Assistant Professor at the Department of Mathematics of the Universidad Técnica Federico Santa María in Santiago, Chile. He did his Ph.D. thesis under the supervision of Patrick L. Combettes in Paris 6 and he works on splitting algorithms for solving monotone inclusions and optimization problems. These methods has been applied to image processing, mean field games, game theory, traffic theory, among other disciplines.

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