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Semi-Infinite Programming and Applications to Minimax Problems

Author

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  • Stanislav Žaković
  • Berc Rustem

Abstract

A minimisation problem with infinitely many constraints – semi-infinite programming problem (SIP) is considered. The problem is solved using a two stage procedure that searches for global maximum violation of the constraints. A version of the algorithm that searches for any violation of constraints is also considered, and the performance of the two algorithm is compared. An application to solving minimax problem (with and without coupled constraints) is given and a comparison with the algorithm for continuous minimax of Rustem and Howe (2001) is included. Finally, we consider an application to chemical engineering problems. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Stanislav Žaković & Berc Rustem, 2003. "Semi-Infinite Programming and Applications to Minimax Problems," Annals of Operations Research, Springer, vol. 124(1), pages 81-110, November.
    • Handle: RePEc:spr:annopr:v:124:y:2003:i:1:p:81-110:10.1023/b:anor.0000004764.76984.30
    DOI: 10.1023/B:ANOR.0000004764.76984.30
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    Citations

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    Cited by:

    1. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    2. P. Parpas & B. Rustem, 2009. "An Algorithm for the Global Optimization of a Class of Continuous Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 461-473, May.
    3. Tadeusz Antczak & Najeeb Abdulaleem, 2021. "E-differentiable minimax programming under E-convexity," Annals of Operations Research, Springer, vol. 300(1), pages 1-22, May.
    4. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Adaptive Bundle Methods for Nonlinear Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2106-2124, July.
    5. Raffaello Seri & Christine Choirat, 2013. "Scenario Approximation of Robust and Chance-Constrained Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 590-614, August.
    6. Michalis Kapsos & Nicos Christofides & Berc Rustem, 2018. "Robust risk budgeting," Annals of Operations Research, Springer, vol. 266(1), pages 199-221, July.
    7. Li-Ping Pang & Qi Wu & Jin-He Wang & Qiong Wu, 2020. "A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods," Computational Optimization and Applications, Springer, vol. 76(1), pages 125-153, May.

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    Keywords

    minimax problems; multiple solutions;

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