A first-order method for nonconvex-strongly-concave constrained minimax optimization

Optimization methods & software 2026

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Authors: Zhaosong Lu, Sanyou Mei
DOI: 10.1080/10556788.2025.2612350
Cited by: 0
References: 25

Abstract

In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax problems and suitably solved by a first-order method developed in this paper that leverages the strong concavity structure. Under suitable assumptions, the proposed method achieves an operation complexity of O(ε−3.5log⁡ε−1), measured in terms of its fundamental operations, for finding an ε-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of ε−0.5.

Fields of Study & Subjects

Optimization and Variational Analysis Advanced Optimization Algorithms Research Stochastic Gradient Optimization Techniques

Publication details

Journal / source
Optimization methods & software
Volume
41
Issue
1
Pages
192–225
Publication date
2 January 2026
Language
EN