Noticias en español
Analysing necessary optimality conditions for a time optimal control problem in Wasserstein spaces.
Abstract: We are interested in developing necessary optimality conditions in the form of a Pontryagin maximum principle for the minimal time Bolza optimal control problem with constraints in the final time. In this problem, the dynamic is given by a non-local continuity equation in the Wasserstein space of probability measures, the set of controls are taken in open-loop form and the set of constraints is represented by functional inequalities applied to the terminal time. To this end, we relate the main challenges of this problem from which a fair amount is accounted by the fact that...
Read MoreProgramación de estados cuánticos con pulsos.
Resumen: En esta charla autocontenida, presentaremos una introducción a los fundamentos de la mecánica cuántica y computación cuántica. Además, introduciremos la nueva forma de controlar computadores cuánticos superconductores, la cual reemplaza a las compuertas cuánticas tradicionales por pulsos electromagnéticos arbitrarios.
Read MoreA second-order descent method with active-set prediction for group sparse optimization.
Abstract: In this talk, we propose a second-order algorithm for the solution of finite and infinite dimensional group sparse optimization problems. Group sparse optimization has gained a lot of attention in the last years due to several important classification problems requiring group sparse solutions. The most prominent application example is the group LASSO problem, which consists in minimizing a least-squares fitting term together with the group sparsity l1/l2 norm. The method is built upon the steepest descent directions of the nonsmooth problem, which are further modified by using...
Read MorePartially non-convex minimax theorem and applications to remotal sets.
Abstract: Given a convex subset B A of a locally convex space Y X; and a function f : Y X ! R such that B is compact and f (y; ); y 2 Y; are concave and upper semicontinuous, we establish in a Örst step a minimax inequality of the form maxy2B infx2A f (y; x) infx2A supy2B0 f (y; x); where B0 is the set of points y 2 B such that f (y; ) is proper and convex. The main di§erence with the classical minimax theorem is that, here, the set B0 does not need to be convex or compact. We use this result to give a new proof of the characterization of remotal sets, relying on the convexiy of the set...
Read MoreGlobalization of the SCD semismooth* Newton method in nonsmooth nonconvex optimization
Abstract: We consider the problem of minimizing an lsc proper function. A locally superlinearly convergent method is given by the SCD (Subspace Containing Derivative) semismooth* Newton method for solving the first order necessary optimality conditions. We will discuss how to compute the SC derivative of the subdifferential mapping defining the linear system for the Newton direction. In order to globalize the SCD semismooth* Newton method, we combine it with some variant of the proximal gradient algorithm. We are able to show that every accumulation point of the sequence produced by our...
Read MoreAproximación de juegos de campo medio de primer orden.
Resumen: Esta charla concierne la aproximación de juegos de campo medio de primer orden, o deterministas, introducidos por J.-M. Lasry y P.-L. Lions en el año 2007. Luego de introducir este tipo de juegos, nos concentraremos en la aproximación de la función valor de un jugador típico, elemento clave de la discretización del juego de campo medio. Esta última puede interpretarse como un juego de campo medio en tiempo discreto y espacio de estados finitos introducido por Gomes, Mohr y Souza en el año 2010. Luego de enunciar el teorema de convergencia principal, terminaremos la charla con...
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