Generalized Nash equilibrium problems with quasi-linear constraints
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929363291734016 |
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| author | Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan |
| author_facet | Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan |
| contents | We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs, the KKT sets can be represented as unions of simpler sets by Carathéodory's theorem. We give a convenient representation for KKT sets using partial Lagrange multiplier expressions. This produces a set of branch polynomial optimization problems, which can be efficiently solved by Moment-SOS relaxations. By doing this, we can compute all generalized Nash equilibria or detect their nonexistence. Numerical experiments are also provided to demonstrate the computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Nash equilibrium problems with quasi-linear constraints Choi, Jiyoung Nie, Jiawang Tang, Xindong Zhong, Suhan Optimization and Control 90C23, 90C33, 91A10, 65K05 We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs, the KKT sets can be represented as unions of simpler sets by Carathéodory's theorem. We give a convenient representation for KKT sets using partial Lagrange multiplier expressions. This produces a set of branch polynomial optimization problems, which can be efficiently solved by Moment-SOS relaxations. By doing this, we can compute all generalized Nash equilibria or detect their nonexistence. Numerical experiments are also provided to demonstrate the computational efficiency. |
| title | Generalized Nash equilibrium problems with quasi-linear constraints |
| topic | Optimization and Control 90C23, 90C33, 91A10, 65K05 |
| url | https://arxiv.org/abs/2405.03926 |