Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems

ArXi:2605.08006v1 Announce Type: cross We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel optimization and minimax optimization separately, existing methods mainly focus on bilevel optimization with lower-level minimization problems, often under strong convexity assumptions, and are not directly applicable to the minimax lower-level setting considered here.