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Optimality Analysis of a Class of Semi-infinite Programming Problems

Author

Listed:
  • Zhi Guo Feng

    (Guangdong Ocean University)

  • Fei Chen

    (Chongqing Normal University)

  • Lin Chen

    (Chongqing Normal University
    University of Electronic Science and Technology of China)

  • Ka Fai Cedric Yiu

    (Hong Kong Polytechnic University)

Abstract

In this paper, we consider a class of semi-infinite programming problems with a parameter. As the parameter increases, we prove that the optimal values decrease monotonically. Moreover, the limit of the sequence of optimal values exists as the parameter tends to infinity. In finding the limit, we decompose the original optimization problem into a series of subproblems. By calculating the maximum optimal values to the subproblems and applying a fixed-point theorem, we prove that the obtained maximum value is exactly the limit of the sequence of optimal values under certain conditions. As a result, the limit can be obtained efficiently by solving a series of simplified subproblems. Numerical examples are provided to verify the limit obtained by the proposed method.

Suggested Citation

  • Zhi Guo Feng & Fei Chen & Lin Chen & Ka Fai Cedric Yiu, 2020. "Optimality Analysis of a Class of Semi-infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 398-411, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01708-8
    DOI: 10.1007/s10957-020-01708-8
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    References listed on IDEAS

    as
    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. Zhi Guo Feng & Ka Fai Cedric Yiu & Sven Erik Nordholm, 2015. "Performance Limit of Broadband Beamformer Designs in Space and Frequency," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 316-341, January.
    3. Ting-Jang Shiu & Soon-Yi Wu, 2012. "Relaxed cutting plane method with convexification for solving nonlinear semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 91-113, September.
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