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An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem

Author

Listed:
  • Weiwei Pan

    (Shanghai University)

  • Jingjing Shen

    (Shanghai University)

  • Zi Xu

    (Shanghai University)

Abstract

In this paper, we study the minimax optimization problem that is nonconvex in one variable and linear in the other variable, which is a special case of nonconvex-concave minimax problem, which has attracted significant attention lately due to their applications in modern machine learning tasks, signal processing and many other fields. We propose a new alternating gradient projection algorithm and prove that it can find an $$\varepsilon$$ ε -first-order stationary solution within $${\mathcal {O}}\left( \varepsilon ^{-3}\right)$$ O ε - 3 projected gradient step evaluations. Moreover, we apply it to solve the weighted maximin dispersion problem and the numerical results show that the proposed algorithm outperforms the state-of-the-art algorithms.

Suggested Citation

  • Weiwei Pan & Jingjing Shen & Zi Xu, 2021. "An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem," Computational Optimization and Applications, Springer, vol. 78(1), pages 287-306, January.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:1:d:10.1007_s10589-020-00237-4
    DOI: 10.1007/s10589-020-00237-4
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    Cited by:

    1. Lingzi Jin & Xiao Wang, 2022. "A stochastic primal-dual method for a class of nonconvex constrained optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 143-180, September.
    2. Siwen Wang & Zi Xu, 2021. "New Approximation Algorithms for Weighted Maximin Dispersion Problem with Box or Ball Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 524-539, August.

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