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

Weiwei Pan, Jingjing Shen and Zi Xu ()
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Weiwei Pan: Shanghai University
Jingjing Shen: Shanghai University
Zi Xu: Shanghai University

Computational Optimization and Applications, 2021, vol. 78, issue 1, No 10, 287-306

Abstract: 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.

Keywords: Nonconvex-linear minimax problem; Complexity analysis; Weighted maximin dispersion problem (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-020-00237-4

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