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Organizing Commitee: María J. Cánovas and Juan Parra, UMH

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El CIO, uno de los catorce institutos universitario de investigación en matemáticas de España, acogerá el próximo 26 de febrero el X Seminario Internacional en Optimización y Análisis Variacional. El evento se desarrollará a lo largo de la mañana en la aula 0.1 del Edificio Torretamarit de la UMH y está dirigido tanto a investigadores como a estudiantes interesados en la temática.

El encuentro dará comienzo a las 11:00 horas con el welcoming coffee y, posteriormente, dará comienzo la primera ponencia, que lleva por título Lipschitz Modulus of Linear and Convex Inequality Systems with the Hausdorff metric impartida por el investigador Marco A. López, de la Universidad de Alicante. This talk analyzes the Lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in Rⁿ. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of Rn+1. In this framework the size of perturbations is measured by means of the (extended) Hausdorff distance. A direct antecedent, extensively studied in the literature, comes from considering the parameter space of all linear systems with a fixed index set, T, where the Chebyshev (extended) distance is used to measure perturbations. In the talk we propose an appropriate indexation strategy which allows us to establish the equality of the Lipschitz moduli of the feasible set mappings in both parametric contexts, as well as to benefit from existing results in the Chebyshev setting for transferring them to the Hausdorff one. In a second stage, the possibility of perturbing directly the set of coefficient vectors of a linear system leads to new contributions on the Lipschitz behavior of convex systems via linearization techniques.
El investigador Matías Raja, de la Universidad de Murcia, tomará el relevo a las 11:155 con la ponencia ‘Super weakly compact sets and their applications’. The aim of this talk is to introduce an interesting class of sets in Banach spaces lying between the norm compact and the weakly compact sets. The motivation for this class arises from the desire to extend the nice properties of uniformly convex spaces to a localised setting. Although most of the theory developed around super weak compactness is linear, together with Gilles Lancien we have addressed the non linear theory too.
Tras una breve pausa, el evento se reanudará a las 12:40 horas con la ponencia ‘Optimality Conditions for Nonlinear Conic Programs via Squared Slack Variables’, del investigador Masao Fukushimam, de la Nanzan University, Japan. Nonlinear symmetric cone programs (NSCPs) constitute a general and important class of optimization problems that contains as special cases nonlinear semidefinite programs (NSDPs), nonlinear second order cone programs (NSOCPs) and traditional nonlinear programs (NLPs). We consider reformulating an NSCP as an ordinary NLP by means of squared slack variables. It is clear that the reformulated NLP is equivalent to the original NSCP in terms of not only global but also local optimality. This, however, is not the case in regard to optimality conditions. We discuss the first-order, i.e., Karush-Kuhn-Tucker (KKT) conditions and, in particular, the second-order necessary conditions as well as sufficient conditions for the NSCP and the reformulated NLP. Working with the reformulated NLP enables us to obtain the second-order optimality conditions for NSCPs in an easy manner, thereby bypassing a number of difficulties associated to the usual variational analytical approach. We also mention the possibility of importing convergence results from nonlinear programming, which we illustrate by means of a simple augmented Lagrangian method for NSCPs
El encargado de concluir el evento será el investigador Francisco J. Aragón  de la Universidad de Alicante, con la ponencia ‘The Boosted DC Algorithm for linearly constrained DC programming’ .The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation step from the point computed by DCA via a line search procedure. In addition, empirical results have shown that BDCA has better chances to escape from bad local optima toward solutions with a better objective value than the classical DCA. In this talk we will show how to extend BDCA to solve a class of DC programs with linear constraints. We propose a new variant of BDCA and establish its global convergence to a critical point. Finally, we present some numerical experiments demonstrating that this new variant of BDCA outperforms DCA both in running time and objective value of the solutions obtained.This is a joint work with R. Campoy and P. T. Vuong


El CIO acoge el X Seminario Internacional en Optimización y Análisis Variacional | Instituto CIO · 21 febrero, 2020 at 11:29 am

[…] Consulta toda la información del evento en: http://cio.umh.es/ova10/ […]

X Seminario Internacional en Optimización y Análisis Variacional – Servicio de Comunicación · 25 febrero, 2020 at 9:50 am

[…] La actividad está dirigida tanto a investigadores como a estudiantes interesados en la temática. Más información del evento en: http://cio.umh.es/ova10/ […]

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