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

Author

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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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    References listed on IDEAS

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    1. Xiaoqi Yang & Zhangyou Chen & Jinchuan Zhou, 2016. "Optimality Conditions for Semi-Infinite and Generalized Semi-Infinite Programs Via Lower Order Exact Penalty Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 984-1012, June.
    2. Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    3. Carl Eggen & Oliver Stein & Stefan Volkwein, 2025. "Granularity for Mixed-Integer Polynomial Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-24, May.
    4. Winterfeld, Anton, 2008. "Application of general semi-infinite programming to lapidary cutting problems," European Journal of Operational Research, Elsevier, vol. 191(3), pages 838-854, December.
    5. O. Stein & A. Winterfeld, 2010. "Feasible Method for Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 419-443, August.
    6. Li Wang & Feng Guo, 2014. "Semidefinite relaxations for semi-infinite polynomial programming," Computational Optimization and Applications, Springer, vol. 58(1), pages 133-159, May.
    7. Haolin Ruan & Zhi Chen & Chin Pang Ho, 2023. "Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1002-1023, September.
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