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<p>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 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.</p>

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Polynomial optimization relaxations for generalized semi-infinite programs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月18日

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  • Xiaomeng Hu,
  • Jiawang Nie

摘要

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 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.