Noticias en español
TITULO A proximal splitting method to solve some stationary mean field game systems
RESUMEN: In this talk we present a proximal splitting method to solve a discretized version of a mean field game problem with local interactions, introduced by Achdou et al. The presence of local interactions imply that, at the continuous level, the mean field game system can be formally obtained as the optimality condition of an associated variational problem. The same argument applies in the discretized version. However, since one of the term in the cost is only sub-differentiable, a suitable splitting method is used in order to obtain a globally convergent...
Read More“Smoothness of the Metric Projection onto Nonconvex Bodies in Hilbert Spaces”
Abstract: “Based on a fundamental work of R. B. Holmes from 1973, we study differentiability properties of the metric projection onto prox-regular sets. We show that if the set is a nonconvex body with a Cp+1-smooth boundary, then the projection is Cp-smooth near suitable open truncated normal rays, which are determined only by the function of prox-regularity. A local version of the same result is established as well, namely, when the smoothness of the boundary and the prox-regularity of the set are assumed only near a fixed point.”
Read MoreFully convex optimal control problems and impulsive systems.
Abstract: We are interested in fully convex optimal control problems, that is, problems whose Lagrangian is jointly convex in the state and the velocity. Problems of this kind have been widely investigated by Rockafellar and collaborators in the absence of state constraints. In particular, it has been established that the adjoint state (which is an absolutely continuous arc as well as the state of the system) solves a dual optimal control problem, and that the dual value function is the conjugate function of the primal value function. In this talk, we discuss properties of the primal...
Read More(Sub-)Gradient formulae for probability functions with applications to power management.
Resumen: Given a parameter-dependent random inequality system a probability function assigns to the parameter the probability of satisfying this system. Such functions play a fundamental role in defining so-called probabilistic or chance constraints as they arise in numerous engineering problems (e.g. hydro reservoir management under uncertain inflows or gas network managment under uncertain demand). Probability functions exhibit some inherent nonsmoothness even if the input data (random inequality system and density of the random distribution) are smooth. Hence the application...
Read MoreStability in shape optimization with second variation
Resumen : This is a joint work with Jimmy Lamboley from University Paris Dauphine. We are interested in the question of stability in the eld of shape optimization. Precisely, we prove that under structural assumptions on the hessian of the considered shape functions, the necessary second order minimality conditions imply that the shape hessian is coercive for a given norm. Moreover, under an additional continuity condition for the second order derivatives, we derive precise optimality results in the class of regular perturbations of a domain. These conditions are quite general...
Read MoreOn optimal transport under the causality constraint.
Abstract: In this talk we shall examine causal transports and the associated optimal transportation problem under the causality constraint (Pc). Loosely speaking, causal transports are a relaxation of adapted processes in the same sense as Kantorovich transport plans are the extension of Monge-type transport maps. We will establish a simple primal-dual picture of both (Pc) and the so-called bicausal transportation problem (whereby causality runs in both directions) in euclidean space or equiv. for discrete-time processes. Together with this, we provide a dynamic programming principle...
Read More