Collolquium Mathematics - Prof. dr. J. Peypouquet University of Chile

Title: Inertial proximal algorithms and variational inequalities

Abstract:

We present a Regularized Inertial Proximal Algorithm to solve convex optimization problems and variational inequalities. It is obtained by means of a convenient finite-difference discretization of a second-order differential equation with vanishing damping, governed by the Yosida regularization of a maximally monotone operator with time-varying index. The first part of the presentation will be devoted to the relationship between the keynote convex optimization algorithms and continuous-time dynamical systems governed by differential equations and inclusions, with and without inertial features. In the second part, I will discuss the difficulties in extending these ideas to variational inequalities that do not arise naturally as convex optimization problems, then present a new model combining regularization and inertia, and finally mention some ongoing and future lines of research in this topic.

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