A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games

Fuente: arXiv
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Main Authors: Baghbadorani, Reza Rahimi, Benenati, Emilio, Grammatico, Sergio
Format: Preprint
Published: 2025
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author Baghbadorani, Reza Rahimi
Benenati, Emilio
Grammatico, Sergio
author_facet Baghbadorani, Reza Rahimi
Benenati, Emilio
Grammatico, Sergio
contents This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a solution algorithm with linear convergence rate. The fast convergence of the method enables receding-horizon control architectures. Furthermore, we demonstrate that {the associated VI admits a closed-form solution within a neighborhood of the attractor, thus allowing for a further reduction in computation time.} Finally, we benchmark the proposed method via numerical experiments in an automated driving application.
format Preprint
id arxiv_https___arxiv_org_abs_2504_05757
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
Baghbadorani, Reza Rahimi
Benenati, Emilio
Grammatico, Sergio
Systems and Control
Optimization and Control
This paper considers constrained linear dynamic games with quadratic objective functions, which can be cast as affine variational inequalities. By leveraging the problem structure, we apply the Douglas-Rachford splitting, which generates a solution algorithm with linear convergence rate. The fast convergence of the method enables receding-horizon control architectures. Furthermore, we demonstrate that {the associated VI admits a closed-form solution within a neighborhood of the attractor, thus allowing for a further reduction in computation time.} Finally, we benchmark the proposed method via numerical experiments in an automated driving application.
title A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
topic Systems and Control
Optimization and Control
url https://arxiv.org/abs/2504.05757