Optimization and Equilibrium

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.

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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,...

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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...

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Enlargements of the Moreau-Rockafellar Subdifferential.

Event Date: Jul 15, 2020 in Optimization and Equilibrium, Seminars

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...

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A general asymptotic function with applications

Event Date: Jul 01, 2020 in Optimization and Equilibrium, Seminars

Abstract: Due to its definition through the epigraph, the usual asymptotic function of convex analysis is a very effective tool for studying minimization, especially of a convex function. However, it is not as convenient, if one wants to study maximization of a function “f”; this is done usually through the hypograph or, equivalently, through “−f”. We introduce a new concept of asymptotic function which allows us to simultaneously study convex and concave functions as well as quasi-convex and quasi-concave functions. We provide some calculus rules and relevant...

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Characterizing the calmness property in convex semi-infinite optimization. Modulus estimates

Event Date: Jun 03, 2020 in Optimization and Equilibrium, Seminars

Abstract: We present an overview of the main results on calmness in convex semi-infinite optimization. The first part addresses the calmness of the feasible set and the optimal set mappings for the linear semi-infinite optimization problem in the setting of canonical perturbations, and also in the framework of full perturbations. While there exists a clear proportionality between the calmness moduli of the feasible set mappings in both contexts, the analysis of the relationship between the calmness moduli of the argmin mappings is much more complicated. Point-based expressions (only...

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