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Related papers: Linear-Quadratic Mean Field Control with Non-Conve…

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In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique…

Optimization and Control · Mathematics 2025-03-04 Jie Xiong , Wen Xu , Ying Yang

This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution…

Optimization and Control · Mathematics 2023-02-22 Henk J. van Waarde , M. Kanat Camlibel , Jaap Eising , Harry L. Trentelman

We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents…

Systems and Control · Computer Science 2020-06-15 Dena Firoozi , Sebastian Jaimungal , Peter E. Caines

We examine mean field control problems on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a…

Optimization and Control · Mathematics 2021-03-29 Alekos Cecchin

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

Optimization and Control · Mathematics 2023-08-23 Pierre-Cyril Aubin-Frankowski , Alain Bensoussan

This paper studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the social control problem, we first obtain a set of forward-backward…

Optimization and Control · Mathematics 2019-04-17 Bingchang Wang , Huanshui Zhang

A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…

Optimization and Control · Mathematics 2016-07-01 J. J. Trujillo , V. M. Ungureanu

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 Hamilton-Jacobi-Bellman equation is solved, for a terminal…

Optimization and Control · Mathematics 2017-03-30 Laurent Pfeiffer

We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In…

Optimization and Control · Mathematics 2026-03-24 Pierre Cardaliaguet , Joe Jackson , Panagiotis E. Souganidis

We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new…

Optimization and Control · Mathematics 2025-12-30 Anna de Crescenzo , Filippo de Feo , Huyên Pham

This paper is concerned with the open-loop time-consistent solution of time-inconsistent mean-field stochastic linear-quadratic optimal control. Different from standard stochastic linear-quadratic problems, both the system matrices and the…

Optimization and Control · Mathematics 2016-08-19 Yuan-Hua Ni , Ji-Feng Zhang , Miroslav Krstic

A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their…

Optimization and Control · Mathematics 2020-12-04 Jalal Arabneydi , Aditya Mahajan

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex…

Optimization and Control · Mathematics 2017-10-10 Ying Hu , Jianhui Huang , Tianyang Nie

In this paper, we prove the existence of classical solutions for time dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses…

Analysis of PDEs · Mathematics 2015-02-27 Diogo Aguiar Gomes , Edgard Almeida Pimentel

We consider team optimal control of decentralized systems with linear dynamics, quadratic costs, and arbitrary disturbance that consist of multiple sub-populations with exchangeable agents (i.e., exchanging two agents within the same…

Systems and Control · Computer Science 2018-09-19 Jalal Arabneydi , Aditya Mahajan

We develop the theory of linear-quadratic (LQ) mean field games (MFGs) in Hilbert spaces with common noise modeled by an infinite-dimensional Wiener process that affects the dynamics of all agents. In the presence of common noise, the…

Optimization and Control · Mathematics 2026-05-28 Hanchao Liu , Dena Firoozi

This paper considers linear quadratic (LQ) mean field games with a major player and analyzes an asymptotic solvability problem. It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique…

Optimization and Control · Mathematics 2019-09-04 Yan Ma , Minyi Huang

We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…

Analysis of PDEs · Mathematics 2020-09-28 Pierre Cardaliaguet , Panagiotis Souganidis

This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main…

Optimization and Control · Mathematics 2020-10-19 Xiao Ma , Qingyuan Qi , Xun Li , Huanshui Zhang

This paper studies linear quadratic Gaussian robust mean field social control problems in the presence of multiplicative noise. We aim to compute asymptotic decentralized strategies without requiring full prior knowledge of agents'…

Systems and Control · Electrical Eng. & Systems 2025-09-16 Zhenhui Xu , Jiayu Chen , Bing-Chang Wang , Yuhu Wu , Tielong Shen