26 citations · 111 across the 20 of their papers we have counts for
23 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…
Generalized conditional gradient and learning in potential mean field games
Pierre Lavigne, Laurent Pfeiffer
We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorit…
Decomposed resolution of finite-state aggregative optimal control problems
Kang Liu, Nadia Oudjane, Laurent Pfeiffer
A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an…
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…
A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints
Joseph Frédéric Bonnans, Justina Gianatti, Laurent Pfeiffer
The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a co…
Weak Solutions for Potential Mean Field Games of Controls
Jameson Graber, Alan Mullenix, Laurent Pfeiffer
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many neg…
Duality and approximation of stochastic optimal control problems under expectation constraints
Laurent Pfeiffer, Xiaolu Tan, Yulong Zhou
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Un…
Discrete-time mean field games with risk averse-agents
J. Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer
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 Kol…
Second-order analysis for the time crisis problem
Laurent Pfeiffer, Terence Bayen
In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in mi…
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…
Feedback Stabilization of the Two-Dimensional Navier-Stokes Equations by Value Function Approximation
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
The value function associated with an optimal control problem subject to the Navier-Stokes equations in dimension two is analyzed. Its smoothness is established around a steady sta…
The Effect of the Terminal Penalty in Receding Horizon Control for a Class of Stabilization Problems
Karl Kunisch, Laurent Pfeiffer
The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are nume…
On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems
Tobias Breiten, Laurent Pfeiffer
Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control probl…
Optimality Conditions in Variational Form for Non-Linear Constrained Stochastic Control Problems
Laurent Pfeiffer
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function…
Optimal control problem for systems of conservation laws, with geometric parameter, and application to the Shallow-Water Equations
Sébastien Court, Karl Kunisch, Laurent Pfeiffer
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic c…
Numerical Study of Polynomial Feedback Laws for a Bilinear Control Problem
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equil…
Control Strategies for the Fokker-Planck Equation
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
Using a projection-based decoupling of the Fokker-Planck equation, control strategies that allow to speed up the convergence to the stationary distribution are investigated. By mea…
Taylor Expansions of the Value Function Associated with a Bilinear Optimal Control Problem
Tobias Breiten, Karl Kunisch, Laurent Pfeiffer
A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived a…
Numerical Methods for Mean-Field-Type Optimal Control Problems
Laurent Pfeiffer
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilto…
Hybrid Optimal Control Problems for a Class of Semilinear Parabolic Equations
Sébastien Court, Karl Kunisch, Laurent Pfeiffer
A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which t…
Optimal Control for a Class of Infinite Dimensional Systems Involving an -term in the Cost Functional
Sébastien Court, Karl Kunisch, Laurent Pfeiffer
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, a…