54 citations · 106 across the 7 of their papers we have counts for
9 papers
Error estimates of a theta-scheme for second-order mean field games
J. Frédéric Bonnans, Kang Liu, Laurent Pfeiffer
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…
Well-posedness of the shooting algorithm for control-affine problems with a scalar state constraint
M. S. Aronna, F. Bonnans, B. S. Goh
We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this…
Large-scale nonconvex optimization: randomization, gap estimation, and numerical resolution
J. Frédéric Bonnans, Kang Liu, Nadia Oudjane +2
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…
Generalized conditional gradient and learning in potential mean field games
J Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer
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 learnin…
Discrete potential mean field games: duality and numerical resolution
J. Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer
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 thro…
Decomposition of convex high dimensional aggregative stochasticcontrol problems
Adrien Séguret, Clémence Alasseur, J. Frédéric Bonnans +3
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 m…
Schauder Estimates for a Class of Potential Mean Field Games of Controls
J. Frédéric Bonnans, Saeed Hadikhanloo, Laurent Pfeiffer
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 a…
A shooting algorithm for problems with singular arcs
Maria Soledad Aronna, J. Frederic Bonnans, Pierre Martinon
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 cas…
Quadratic order conditions for bang-singular extremals
Maria Soledad Aronna, J. Frederic Bonnans, Andrei V. Dmitruk +1
This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and ineq…