An Inexact Bundle Method for Semi-Infinite Minimax Problems

Tianyou Shang (), Ke Su, Yanshu Wei () and Bing Zhao ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 03, 1-19

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.

Keywords: Semi-infinite minimax; nonsmooth optimization; bundle method; inexact information (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0217595924500192

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