Optimization and Equilibrium

Sigma-convex functions and Sigma-subdifferentials.

Event Date: Sep 23, 2020 in Optimization and Equilibrium, Seminars

Abstract:  In this talk we present and study the notion of $\sigma$-subdifferential of a proper function $f$ which contains theClarke-Rockafellar subdifferential of $f$ under some mild assumptions on $f$. We show that some well known properties of the convex function, namely Lipschitz property in the interior of its domain, remain valid for thelarge class of $\sigma$-convex functions.

Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization.

Event Date: Sep 02, 2020 in Optimization and Equilibrium, Seminars

Abstract: This talk aims at developing two versions of the generalized Newton method to compute local minimizers for nonsmooth problems of unconstrained and constraned optimization that satisfy an important stability property known as tilt stability. We start with unconstrained minimization of continuously differentiable cost functions having Lipschitzian gradients and suggest two second-order algorithms of the Newton type: one involving coderivatives of Lipschitzian gradient mappings, and the other based on graphical derivatives of the latter. Then we proceed with the propagation of these...

An overview of Sweeping Processes with applications.

Event Date: Aug 26, 2020 in Optimization and Equilibrium, Seminars

Abstract: The Moreau’s Sweeping Process is a first-order differential inclusion, involving the normal cone to a moving set depending on time. It was introduced and deeply studied by J.J. Moreau in the 1970s as a model for an elastoplastic mechanical system. Since then, many other applications have been given, and new variants have appeared. In this talk, we review the latest developments in the theory of sweeping processes and its variants. We highlight open questions and provide some applications.

Epi-convergence, asymptotic analysis and stability in set optimization problems.

Event Date: Aug 05, 2020 in Optimization and Equilibrium, Seminars

Abstract: We study the stability of set optimization problems with data that are not necessarily bounded. To do this, we use the well-known notion of epi-convergence coupled with asymptotic tools for set-valued maps. We derive characterizations for this notion that allows us to study the stability of vector and set type solutions by considering variations of the whole data (feasible set and objective map). We extend the notion of total epi-convergence to set-valued maps. * This work has been supported by Conicyt-Chile under project FONDECYT 1181368 Joint work with Elvira Hérnández,...

Satisfying Instead of Optimizing in the Nash Demand Games.

Event Date: Jul 22, 2020 in Optimization and Equilibrium, Seminars

Abstract:   The Nash Demand Game (NDG) has been one of the first models (Nash 1953) that has tried to describe the process of negotiation, competition, and cooperation. This model is still subject to active research, in fact, it maintains a set of open questions regarding how agents optimally select their decisions and how they face uncertainty.   However, the agents act rather guided by chance and necessity, with a Darwinian flavor. Satisfying, instead of optimising. The Viability Theory (VT) has this approach. Therefore, we investigate the NDG under this point of view. In...

Abstract: The Moreau–Rockafellar subdifferential is a highly important notion in convex analysis and optimization theory.  But there are many functions which fail to be subdifferentiable at certain points. In particular, there is a continuous convex function defined on $\ell^2(\mathbb{N})$, whose Moreau–Rockafellar subdifferential is empty at every point of its domain. This talk  proposes some enlargements of  the Moreau—Rockafellar subdifferential: the sup$^\star$-sub\-differential,  sup-subdifferential and   symmetric subdifferential, all of them being nonempty for the...