# Optimization and Equilibrium

## Large ranking games with diffusion control & Optimal control of the Sweeping Process with a non-smooth moving set.

Event Date: Oct 05, 2022 in Optimization and Equilibrium, Seminars

Title : Large ranking games with diffusion control. Abstract : We consider a symmetric stochastic differential game where each player can control the diffusion intensity of an individual dynamic state process. The players whose states at a deterministic finite time horizon are among the best α ∈ (0, 1) of all states receive a fixed prize. In order to find an equilibrium, we first focus on the version of this game where the number of players tend to infinity. Within the mean field limit version of the game we compute an explicit equilibrium, a threshold strategy that consists in choosing the...

## Multidimensional Apportionment Through Discrepancy Theory. & Determination of functions by the metric slope.

Event Date: Aug 24, 2022 in Optimization and Equilibrium, Seminars

Speaker 1: Víctor Verdugo Title: Multidimensional Apportionment Through Discrepancy Theory. Abstract: Deciding how to allocate the seats of a house of representatives is one of the most fundamental problems in the political organization of societies, and has been widely studied over already two centuries. The idea of proportionality is at the core of most approaches to tackle this problem, and this notion is captured by the divisor methods, such as the Jefferson/D’Hondt method. In a seminal work, Balinski and Demange extended the single-dimensional idea of divisor methods to the...

## 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...

## 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....

## 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).