Optimization and Equilibrium

Constant Rank Conditions for Second-Order Cone and Semidefinite Programming.

Event Date: Jun 01, 2022 in Optimization and Equilibrium, Seminars

Abstract: In the context of the COVID-19, the development of methods to trace the spread of the virus is of vital importance. One of such methods relies on PCR testing of wastewater samples to locate sudden the appearance of infection. Given a representation of the wastewater network as a directed graph, we aim for a strategy that finds a new infected node using the worst-case minimum number of tests. This problem proves to be challenging on networks with uncertainty, as is the case of real-world data. We will explore the connection with other known graph problems and show upper bounds for...

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Continuity and maximal quasimonotonicity of normal cone operators.

Event Date: Dec 01, 2021 in Optimization and Equilibrium, Seminars

Abstract:  In this talk we present some properties of the adjusted normal cone operator of quasiconvex functions. In particular, we introduce a new notion of maximal quasimotonicity for set-valued maps, different from similar ones that appeared recently in the literature, and we show that this operator is maximal quasimonotone in this sense. Among other results, we prove the $s\times w^{\ast}$ cone upper semicontinuity of the normal cone operator in the domain of $f$, in case the set of global minima is empty, or a singleton, or has non empty interior (joint work with M. Bianchi and R....

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Brezis pseudomonotone bifunctions and quasi equilibrium problems via penalization.

Event Date: Dec 15, 2021 in Optimization and Equilibrium, Seminars

Abstract:  We investigate quasi equilibrium problems in a reflexive Banach space under the assumption of Brezis pseudomonotonicity of the function involved. To establish existence results under weak coercivity conditions we replace the quasi equilibrium problem with a sequence of penalized usual equilibrium problems. To deal with the non compact framework, we apply a regularized version of the penalty method. The particular case of set-valued quasi variational inequalities is also considered (Joint work with Monica Bianchi and Gabor Kassay).

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Closedness under addition for families of quasimonotone operators.

Event Date: May 11, 2022 in Optimization and Equilibrium, Seminars

Abstract:  In this talk we will discuss some results about quasimonotone family of operators. For some notions that are extensions of monotoniticity but not beyond quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict quasimonotonicity and proper quasimonotonicity, we will discuss systematically when the sum of two operators satisfying one of those properties, inherits the same property. Several examples showing the optimality in some sense of our results, are presented. Join work with: Fabián Flores-Bazán and Nicolas Hadjisavvas.

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Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methods.

Event Date: Nov 17, 2021 in Optimization and Equilibrium, Seminars

 Abstract: For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear $\mathcal{O}\left(k^{\,-k\left(\frac{p-1}{p+1}\right)}\right)$ global rates for the proposed variants of the A-HPE and large-step A-HPE methods, respectively. The parameter $p\geq 2$ appears in the (high-order) large-step condition of the new large-step A-HPE algorithm. We apply our  results to high-order tensor methods, obtaining a new inexact (relative- error) tensor...

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El Lema de Farkas: Algunas extensiones y aplicaciones.

Event Date: Nov 03, 2021 in Optimization and Equilibrium, Seminars

Abstract:  Tras revisar la versión clásica del lema de Farkas y sus aplicaciones, se presentan algunas extensiones a sistemas con infinitas inecuaciones, con infinitas variables o ambas cosas a la vez, junto con algunas de sus respectivas aplicaciones.

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