# Optimization and Equilibrium

## One-Step Estimation with Scaled Proximal Methods. & Splitting algorithms for monotone inclusions with minimal lifting.

Event Date: Nov 23, 2022 in Optimization and Equilibrium, Seminars

Charla 1:  Abstract: We study statistical estimators computed using iterative optimization methods that are not run until completion. Classical results on maximum likelihood estimators (MLEs) assert that a one-step estimator (OSE), in which a single Newton-Raphson iteration is performed from a starting point with certain properties, is asymptotically equivalent to the MLE. We further develop these early-stopping results by deriving properties of one-step estimators defined by a single iteration of scaled proximal methods. Our main results show the asymptotic equivalence of the...

## Optimization and Economic Equilibrium.

Event Date: Nov 16, 2022 in Optimization and Equilibrium, Seminars

Abstract: In the standard theory of economic equilibrium, various “agents” optimize what they want to buy and sell in order to adjust their holdings on the basis of given prices and associated budget constraints. Their decisions depend on preference relations that are representable nonuniquely by utility functions on the space of goods vectors.  The standard question posed by economists is whether prices exist under which the resulting total demands of the agents are matched by total supplies.  Equilibrium is a state in which, at the given prices, no agent wants to buy or sell...

## 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...

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....