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On Solving the Convex Semi-Infinite Minimax Problems via Superlinear 𝒱𝒰 Incremental Bundle Technique with Partial Inexact Oracle

Author

Listed:
  • Ming Huang

    (School of Science, Dalian Maritime University, Dalian 116026, P. R. China)

  • Jinlong Yuan

    (School of Science, Dalian Maritime University, Dalian 116026, P. R. China)

  • Sida Lin

    (School of Science, Dalian Maritime University, Dalian 116026, P. R. China2School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, P. R. China)

  • Xijun Liang

    (College of Science, China University of Petroleum, Qingdao 266580, P. R. China)

  • Chongyang Liu

    (School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, P. R. China)

Abstract

In this paper, we study convex semi-infinite programming involving minimax problems. One of the difficulties in solving these problems is that the maximum type functions are not differentiable. Due to the nonsmooth nature of the problem, we apply the special proximal bundle scheme on the basis of 𝒱𝒰-decomposition theory to solve the nonsmooth convex semi-infinite minimax problems. The proposed scheme requires an evaluation within some accuracy for all the components of the objective function. Regarding the incremental method, we only need one component function value and one subgradient which are estimated to update the bundle information and produce the search direction. Under some mild assumptions, we present global convergence and local superlinear convergence of the proposed bundle method. Numerical results of several example problems are reported to show the effectiveness of the new scheme.

Suggested Citation

  • Ming Huang & Jinlong Yuan & Sida Lin & Xijun Liang & Chongyang Liu, 2021. "On Solving the Convex Semi-Infinite Minimax Problems via Superlinear 𝒱𝒰 Incremental Bundle Technique with Partial Inexact Oracle," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-32, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400157
    DOI: 10.1142/S0217595921400157
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