Noticias en español
Percolation games.
Abstract: Inspired by first-passage percolation models, we consider zero-sum games on Z^d and study their limit behavior when the game duration tends to infinity. After reviewing several fundamental results in this literature, we present a generalization and discuss connections with long-term behavior of Hamilton-Jacobi equations.
Read MoreRobust shape optimization with small uncertaintie.
Abstract: In this talk, we propose two approaches for dealing with small uncertainties in geometry and topology optimization of structures. Uncertainties occur in the loadings, the material properties, the geometry or the imposed vibration frequency. A first approach, in a worst-case scenario, amounts to linearize the considered cost function with respect to the uncertain parameters, then to consider the supremum function of the obtained linear approximation, which can be rewritten as a more `classical’ function of the design, owing to standard adjoint techniques from optimal control...
Read MoreOne-Step Estimation with Scaled Proximal Methods. & Splitting algorithms for monotone inclusions with minimal lifting.
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...
Read MoreOptimization and Economic Equilibrium.
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...
Read MoreLarge ranking games with diffusion control & Optimal control of the Sweeping Process with a non-smooth moving set.
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...
Read MoreMultidimensional Apportionment Through Discrepancy Theory. & Determination of functions by the metric slope.
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...
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