Related papers: A Douglas-Rachford Splitting Method for Solving Mo…
We provide two weakly convergent algorithms for finding a zero of the sum of a maximally monotone operator, a cocoercive operator, and the normal cone to a closed vector subspace of a real Hilbert space. The methods exploit the intrinsic…
In this paper we propose a new operator splitting algorithm for distributed Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and inertial effects. Our work is inspired by recent deterministic operator splitting…
Finding a zero of a sum of maximally monotone operators is a fundamental problem in modern optimization and nonsmooth analysis. Assuming that resolvents of the operators are available, this problem can be tackled with the Douglas-Rachford…
This paper studies a class of dynamic Stackelberg games under open-loop information structure with constrained linear agent dynamics and quadratic utility functions. We show two important properties for this class of dynamic Stackelberg…
It is common to encounter large-scale monotone inclusion problems where the objective has a finite sum structure. We develop a general framework for variance-reduced forward-backward splitting algorithms for this problem. This framework…
We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…
We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the…
This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact…
We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field…
We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the…
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to…
We consider distributed optimization in the client-server setting. By use of Douglas-Rachford splitting to the dual of the sum problem, we design a BFGS method that requires minimal communication (sending/receiving one vector per round for…
We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one…
Dynamic games can be an effective approach for modeling interactive behavior between multiple competitive agents in autonomous racing and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In…
In this work, we consider the problem of autonomous racing with multiple agents where agents must interact closely and influence each other to compete. We model interactions among agents through a game-theoretical framework and propose an…
We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…
Dynamic games arise when multiple agents with differing objectives control a dynamic system. They model a wide variety of applications in economics, defense, energy systems and etc. However, compared to single-agent control problems, the…
In this work, we propose solving the Information bottleneck (IB) and Privacy Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a general Markovian information-theoretic Lagrangian that includes IB and PF into a…