A Douglas-Rachford Splitting Method for Solving Monotone Variational Inequalities in Linear-quadratic Dynamic Games
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917423782821888 |
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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 |