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arXiv · 2303.14308

Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs

Xiaomeng Hu·Jiawang Nie
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Abstract

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.

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Xiaomeng Hu, Jiawang Nie. 2023-03-25. Polynomial Optimization Relaxations for Generalized Semi-Infinite Programs. https://arxiv.org/abs/2303.14308

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