Noticias en español
Aproximación de juegos de campo medio de primer orden.
Resumen: Esta charla concierne la aproximación de juegos de campo medio de primer orden, o deterministas, introducidos por J.-M. Lasry y P.-L. Lions en el año 2007. Luego de introducir este tipo de juegos, nos concentraremos en la aproximación de la función valor de un jugador típico, elemento clave de la discretización del juego de campo medio. Esta última puede interpretarse como un juego de campo medio en tiempo discreto y espacio de estados finitos introducido por Gomes, Mohr y Souza en el año 2010. Luego de enunciar el teorema de convergencia principal, terminaremos la charla con...
Read MoreConvergence Rate of Nonconvex Douglas-Rachford splitting via merit functions, with applications to weakly convex constrained optimization.
Abstract: We analyze Douglas-Rachford splitting techniques applied to solving weakly convex optimization problems. Under mild regularity assumptions, and by the token of a suitable merit function, we show convergence to critical points and local linear rates of convergence. The merit function, comparable to the Moreau envelope in Variational Analysis, generates a descent sequence, a feature that allows us to extend to the non-convex setting arguments employed in convex optimization. A by-product of our approach is an ADMM-like method for constrained problems with weakly convex objective...
Read MoreProblem Decomposition in Convex Optimization: Advances Beyond ADMM.
Abstract: Applications of convex optimization in areas like image processing and machine learning have stimulated a huge interest in solution methodology that can take advantage of underlying decomposable structure in a problem, especially when iterations can make good use of “prox” mappings on the problem’s components. Very popular in this development has been the Alternating Direction Method of Multipliers (ADMM). But other approaches that branch out from the same mathematical roots in different modes now offer new advances in the flexibility of problem formulation and...
Read MorePercolation 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...
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