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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.08108 |
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| _version_ | 1866908798805868544 |
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| author | Jardim, Manoel Sagastizábal, Claudia Solodov, Mikhail |
| author_facet | Jardim, Manoel Sagastizábal, Claudia Solodov, Mikhail |
| contents | We propose an algorithm to solve quasi-variational inequality problems, based on the Dantzig-Wolfe decomposition paradigm. Our approach solves in the subproblems variational inequalities, which is a simpler problem, while restricting quasi-variational inequalities in the master subproblems, making them generally (much) smaller in size when the original problem is large-scale. We prove global convergence of our algorithm, assuming that the mapping of the quasi-variational inequality is either single-valued and continuous or it is set-valued maximally monotone. Quasi-variational inequalities serve as a framework for several equilibrium problems, and we apply our algorithm to an important example in the field of economics, namely the Walrasian equilibrium problem formulated as a generalized Nash equilibrium problem. Our numerical assessment demonstrates good performance and usefullness of the approach for the large-scale cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Dantzig-Wolfe Decomposition Method for Quasi-Variational Inequalities Jardim, Manoel Sagastizábal, Claudia Solodov, Mikhail Optimization and Control We propose an algorithm to solve quasi-variational inequality problems, based on the Dantzig-Wolfe decomposition paradigm. Our approach solves in the subproblems variational inequalities, which is a simpler problem, while restricting quasi-variational inequalities in the master subproblems, making them generally (much) smaller in size when the original problem is large-scale. We prove global convergence of our algorithm, assuming that the mapping of the quasi-variational inequality is either single-valued and continuous or it is set-valued maximally monotone. Quasi-variational inequalities serve as a framework for several equilibrium problems, and we apply our algorithm to an important example in the field of economics, namely the Walrasian equilibrium problem formulated as a generalized Nash equilibrium problem. Our numerical assessment demonstrates good performance and usefullness of the approach for the large-scale cases. |
| title | A Dantzig-Wolfe Decomposition Method for Quasi-Variational Inequalities |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.08108 |