Noticias en español
An algebraic view of the smallest strictly monotonic function.
Abstract: The talk concerns with one of the most popular functions to derive nonconvex separation results. Complete characterizations for both its level sets and basic properties such as monotonicity and convexity are provided in terms of its parameters. Most of these characterizations work without considering any additional requirement or assumption. Finally, as an application, a vectorial form of the Ekeland variational principle is provided.
Read MorePrincipal-Agent problem in insurance: from discrete-to continuous-time.
Abstract: In this talk we present a contracting problem between an insurance buyer and the seller, subject to prevention efforts in the form of self-insurance and self-protection. We start with a static formulation, corresponding to an optimization problem with variational inequality constraint, and extend the main properties of the optimal contract to the continuous-time formulation, corresponding to a stochastic control problem in weak form under non-singular measures.
Read MoreSigma-convex functions and Sigma-subdifferentials.
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.
Read MoreGeneralized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization.
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...
Read MoreAn overview of Sweeping Processes with applications.
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.
Read MoreEpi-convergence, asymptotic analysis and stability in set optimization problems.
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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