Noticias en español
“Sufficient optimality conditions hold for almost all nonlinear semidefinite programs”
Abstract: We derive a new genericity result for nonlinear semidefinite programming (NLSDP). Namely, almost all linear perturbations of a given NLSDP are shown to be nondegenerate. Here, nondegeneracy for NLSDP refers to the transversality constraint qualification, strict complementarity and second-order sufficient condition. A reduced NLSDP is locally considered by transforming equivalently thesemidefinite constraint to a smaller dimension via Schur complement. While deriving optimality conditions for the reduced NLSDP, the `$H$-term” in the second-order sufficient condition...
Read MoreAsymptotic properties of an optimization-based matching estimator for average treatment effects
Abstract: This paper investigates the asymptotic properties of a novel matching estimator for the average treatment effects of binary programs. In order to impute the missing potential outcome for each unit, this approach employs both a number of neighbors and a weighting scheme that are endogenously determined by solving a nested pair of optimization problems associated with an individual covariate balancing criterion. Under mild conditions, our main contributions are: (i) the asymptotic normality and a consistent estimator of the conditional variance of the estimators for...
Read MoreOptimal control and Hamilton-Jacobi-Bellman equations. Some extensions to problems on networks
Abstract: The first aim of this talk is to show that, using Variational Analysis tools, it is possible to provide a characterization of the Value Function of an optimal control problem in terms of the Hamilton-Jacobi-Bellman (HJB) equation, meaning that the Value Function is the unique (not necessarily continuous) viscosity solution of the HJB equation. The second goal is to present some new results concerning applications of the techniques mentioned above to optimal control problems whose state is constrained to remain on a network, and whose dynamical system is (possibly)...
Read MorePreservation of geometrical properties under sphericalization and flattening in the metric setting
ABSTRACT: The process of obtaining the Riemann sphere from the complex plane, and viceversa, was generalized in the metric setting by using sphericalization and flattening. These conformal transformations are dual to each other, and the performance of sphericalization followed by flattening, or viceversa, results in a metric space that is bi-Lipschitz equivalent to the original space. A very natural problem is therefore to study which geometric properties are preserved under these transformations. Metric spaces endowed with a doubling measure and supporting a Poincaré inequality are...
Read MoreConvexity of the image of quadratic functions: a geometric point of view
Abstract: The convexity of the image of quadratic functions is crucial when stablishing Farkas-type alternative results (known as s-lemmas in the quadratic context), which are relevant in many applications. A geometric point of view is presented, which strongly relies in the graphic properties of the image of simple sets of $\R^n$. This gives new understanding on the problem, simplifies classical results and leads to new ones, explained in this talk.
Read MoreLow distortion embeddings of metric graphs and linear properties of Banach spaces
Abstract: We will survey examples of metric graphs whose low distortion embeddability into a Banach space X implies various linear properties for X such as non-reflexivity, containement of $\ell_1$ or large Szlenk index. In some cases the implications can be reversed (up to a renorming).
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