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A Global Approach for Generalized Semi-Infinite Programs with Polyhedral Parameter Sets

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  • Xiaomeng Hu

    (University of California San Diego)

  • Jiawang Nie

    (University of California San Diego)

  • Suhan Zhong

    (Texas A&M University)

Abstract

This paper studies generalized semi-infinite programs (GSIPs) defined with polyhedral parameter sets. Assume these GSIPs are given by polynomials. We propose a new approach to solve them as a disjunctive program. This approach is based on the Karush-Kuhn-Tucker (KKT) conditions of the robust constraint and a technique called partial Lagrange multiplier expressions. We summarize a semidefinite algorithm and study its convergence properties. Numerical experiments are given to show the efficiency of our method. In addition, we checked its performance in gemstone cutting and robust control applications.

Suggested Citation

  • Xiaomeng Hu & Jiawang Nie & Suhan Zhong, 2025. "A Global Approach for Generalized Semi-Infinite Programs with Polyhedral Parameter Sets," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-39, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02807-0
    DOI: 10.1007/s10957-025-02807-0
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