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

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 $$\varepsilon$$ -first-order stationary solution within $${\mathcal {O}}\left( \varepsilon ^{-3}\right)$$ 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.