Zobrazeno 1 - 10
of 167
pro vyhledávání: '"Bonnans, J. Frederic"'
We introduce and analyze a new finite-difference scheme, relying on the theta-method, for solving monotone second-order mean field games. These games consist of a coupled system of the Fokker-Planck and the Hamilton-Jacobi-Bellman equation. The theta
Externí odkaz:
http://arxiv.org/abs/2212.08128
We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this problem, obtai
Externí odkaz:
http://arxiv.org/abs/2204.02366
We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step of the gene
Externí odkaz:
http://arxiv.org/abs/2109.05785
We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows hard constr
Externí odkaz:
http://arxiv.org/abs/2106.07463
Autor:
Séguret, Adrien, Alasseur, Clémence, Bonnans, J. Frédéric, De Paola, Antonio, Oudjane, Nadia, Trovato, Vincenzo
Publikováno v:
Applied Mathematics & Optimization, Volume 88, Article number 8, Year 2023
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some reasonable assump
Externí odkaz:
http://arxiv.org/abs/2008.09827
We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by composite ri
Externí odkaz:
http://arxiv.org/abs/2005.02232
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to
Externí odkaz:
http://arxiv.org/abs/1909.05056
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to
Externí odkaz:
http://arxiv.org/abs/1906.00237
An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent involves a price depending at a given time on the controls of all agents and a congestion term. Th
Externí odkaz:
http://arxiv.org/abs/1902.05461
Publikováno v:
Journal of Optimization Theory and Applications 158, 2 (2013) 419-459
In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to
Externí odkaz:
http://arxiv.org/abs/1206.0839