A first-order method for constrained nonconvex-nonconcave minimax optimization

• 成果类型: Article; Early Access
• 署名作者: Lu, Zhaosong; Wang, Xiangyuan
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02415-4
• 发表日期: 2026-08-25
• 关键词: Constrained nonconvex-nonconcave minimax optimization; Local KL condition; Local generalized H & ouml; lder smoothness; Sequential convex programming method; Inexact proximal gradient method; First-order oracle complexity

摘要

We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation satisfies a local Kurdyka-& Lstrok;ojasiewicz (KL) condition, we show that the maximal function of the original problem enjoys a local generalized H & ouml;lder smoothness property. We also propose a sequential convex programming (SCP) method for solving constrained optimization problems and establish its convergence rate under a local KL condition. Leveraging these results, we develop an inexact proximal gradient method for the original minimax problem, where the inexact gradient of the maximal function is computed via the SCP method applied to a locally KL-structured subproblem. Finally, we establish complexity guarantees for the proposed method in computing an approximate stationary point of the original minimax problem.