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

par Luis Briceño (Université Federico Santa María, Chili)

vendredi 17 juin 2016, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

In this talk we provide a survey of convex optimisation algorithms, from the classical steepest descent method and proximal point algorithm, in the case of minimising a single convex function, 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. 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.