An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms

Jiefei He (), Huiling Zhang () and Zi Xu ()
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Jiefei He: Shanghai University
Huiling Zhang: Shanghai University
Zi Xu: Shanghai University

Journal of Global Optimization, 2024, vol. 90, issue 1, No 4, 73-92

Abstract: Abstract Nonconvex minimax problems have attracted significant attention in machine learning, wireless communication and many other fields. In this paper, we propose an efficient approximation proximal gradient algorithm for solving a class of nonsmooth nonconvex-linear minimax problems with a nonconvex nonsmooth term, and the number of iteration to find an $$\varepsilon $$ ε -stationary point is upper bounded by $${\mathcal {O}}(\varepsilon ^{-3})$$ O ( ε - 3 ) . Some numerical results on one-bit precoding problem in massive MIMO system and a distributed non-convex optimization problem demonstrate the effectiveness of the proposed algorithm.

Keywords: Nonconvex-linear minimax problem; Nonsmooth problem; Iteration complexity; Approximation proximal gradient algorithm; 90C47; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-024-01383-3

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