Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913789980442624 |
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| author | Hu, Xiaomeng Nie, Jiawang |
| author_facet | Hu, Xiaomeng Nie, Jiawang |
| contents | This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions. Moment-SOS relaxations are applied to solve the polynomial optimization. The convergence of this hierarchy is shown under certain conditions. In particular, the classical semi-infinite programs (SIPs) can be solved as a special case of GSIPs. We also study GSIPs that have convex infinity constraints and show that they can be solved exactly by a single polynomial optimization relaxation. The computational efficiency is demonstrated by extensive numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs Hu, Xiaomeng Nie, Jiawang Optimization and Control This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions. Moment-SOS relaxations are applied to solve the polynomial optimization. The convergence of this hierarchy is shown under certain conditions. In particular, the classical semi-infinite programs (SIPs) can be solved as a special case of GSIPs. We also study GSIPs that have convex infinity constraints and show that they can be solved exactly by a single polynomial optimization relaxation. The computational efficiency is demonstrated by extensive numerical results. |
| title | Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2303.14308 |