A Newton iteration for differentiable set-valued maps

International audienc

An iterative method for solving H-differentiable inclusions

International audienc

Stability of minimizers of set optimization problems

International audienc

A Lyusternik–Graves theorem for the proximal point method

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (xˉ,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular.Research of the first author was partially supported by Ministerio de Ciencia e Innovación (Spain), grant MTM2008-06695-C03-01 and program “Juan de la Cierva”. Research of the second author was partially supported by Contract EA4540 (France)