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An Inexact Bundle Method for Semi-Infinite Minimax Problems

Author

Listed:
  • Tianyou Shang

    (Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China)

  • Ke Su

    (Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China)

  • Yanshu Wei

    (Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China)

  • Bing Zhao

    (Hebei Key Laboratory of Machine, Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, P. R. China)

Abstract

Semi-infinite minimax problems are widely utilized in various fields; however, there is a scarcity of algorithms that can directly tackle convex-convex and convex-concave semi-infinite minimax problems. An inexact algorithm based on the bundle method is introduced in this paper, which can be directly applied to solve both types of semi-infinite minimax problems. The novel algorithm offers the advantage of not requiring exact solutions for the inner maximization problem but only necessitates optimal solution with a certain level of precision. Additionally, the augmentation function method is employed to address nonconvergence issues encountered in traditional bundle method when dealing with convex-convex minimax problems. Global convergence of our algorithm is proven under reasonable assumptions. Numerical results from several examples demonstrate the effectiveness and practicality of our proposed approach.

Suggested Citation

  • Tianyou Shang & Ke Su & Yanshu Wei & Bing Zhao, 2025. "An Inexact Bundle Method for Semi-Infinite Minimax Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 42(03), pages 1-19, June.
    • Handle: RePEc:wsi:apjorx:v:42:y:2025:i:03:n:s0217595924500192
    DOI: 10.1142/S0217595924500192
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