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The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization

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  • Ke Su
  • Shaohua Liu
  • Wei Lu

Abstract

In this paper, we proposed an adaptive QP-free method without a penalty function or a filter for minimax optimization. In each iteration, solved two linear systems of equations constructed from Lagrange multipliers and KKT-conditioned NCP functions. Based on the work set, the computational scale is further reduced. Instead of the filter structure, we adopt a nonmonotonic equilibrium mechanism with an adaptive parameter adjusted according to the result of each iteration. Feasibility of the algorithm are given, and the convergence under some assumptions is demonstrated. Numerical results and practical application are reported at the end.

Suggested Citation

  • Ke Su & Shaohua Liu & Wei Lu, 2023. "The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization," PLOS ONE, Public Library of Science, vol. 18(7), pages 1-18, July.
    • Handle: RePEc:plo:pone00:0274497
    DOI: 10.1371/journal.pone.0274497
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    References listed on IDEAS

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    1. Jin-bao Jian & Xing-de Mo & Li-juan Qiu & Su-ming Yang & Fu-sheng Wang, 2014. "Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 158-188, January.
    2. E. Obasanjo & G. Tzallas-Regas & B. Rustem, 2010. "An Interior-Point Algorithm for Nonlinear Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 291-318, February.
    3. W. Hare & J. Nutini, 2013. "A derivative-free approximate gradient sampling algorithm for finite minimax problems," Computational Optimization and Applications, Springer, vol. 56(1), pages 1-38, September.
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