Noticias en español
Stochastic incremental mirror descent algorithms with Nesterov smoothing.
Abstract: We propose a stochastic incremental mirror a prox-friendly proper, convex and lower semicontinuous function. Different to the previous cdescent algorithm constructed by means of the Nesterov smoothing for minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space. The algorithm can be adapted in order to minimize (in the same setting) a sum of finitely many proper, convex and lower semicontinuous functions composed with linear operators. Another modification of the scheme leads to a stochastic...
Read MoreConstant Along Primal Rays Conjugacies and the l0 Pseudonorm.
Abstract: he so-called l0 pseudonorm counts the number of nonzero components of a vector. It is standard in sparse optimization problems. However, as it is a discontinuous and nonconvex function, the l0 pseudonorm cannot be satisfactorily handled with the Fenchel conjugacy. In this talk, we present the Euclidean Capra-conjugacy, which is suitable for the l0 pseudonorm, as this latter is “convex” in the sense of generalized convexity (equal to its biconjugate). We immediately derive a convex factorization property (the l0 pseudonorm coincides, on the unit sphere, with a convex lsc function)...
Read MoreOn strongly quasiconvex functions: theory and applications.
Abstract: In this talk, we present a new existence result for the classof lsc strongly quasiconvex functions by showing that every strongly quasiconvex function is 2-supercoercive (in particular, coercive). Furthermore, we investigate the usual properties of proximal operators for strongly quasiconvex functions. In particular, we prove that the set of fixed points of the proximal operator coincides with the unique minimizer of a lsc strongly quasiconvex function. As a consequence, we implemented the proximal point algorithm for finding the unique solution of the minimization problem by...
Read MoreComplejidad en Búsqueda Coordenada de Alto Orden en Bloques.
Abstract: Definimos métodos de alto orden para minimización en cajas con búsqueda coordenada por bloques. Probamos resultados de convergencia y complejidad para puntos estacionarios de alto orden adecuados. Exhibimos ejemplos.
Read MoreOn the construction of maximal p-cyclically monotone operators.
Abstract: In this talk we deal with the construction of explicit examples of maximal p-cyclically maximal monotone operators. To the date, there is only one instance of an explicit example of a maximal 2-cyclically monotone operator that is not maximal monotone. We present several other examples, and a proposal of how such examples can be constructed.
Read MoreOn diametrically maximal sets, maximal premonotone maps and premonotone bifunctions.
Abstract: First, we study diametrically maximal sets in the Euclidean space (those which are not properly contained in a set with the samediameter), establishing their main properties. Then, we use these sets for exhibiting an explicit family of maximal premonotone operators. We also establish some relevant properties of maximal premonotone operators, like their local boundedness, and finally we introduce the notion of premonotone bifunctions, presenting a canonical relation between premonotone operators and bifunctions, that extends the well known one, which holds in the monotone...
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