An adaptive proximal ADMM for nonconvex linearly constrained composite programs
Mathematical Programming, Series A, 2026
We develop an adaptive proximal alternating direction method of multipliers (ADMM) for linearly constrained composite optimization with a smooth, weakly convex component and a convex, block-separable nonsmooth component with compact domain. The method adapts to problem parameters, including smoothness and weak convexity constants, and permits inexact solutions of its block subproblems.
Our analysis establishes iteration complexity guarantees for finding approximate first-order stationary points without rank assumptions on the constraint matrices. These guarantees match the best available bounds for proximal ADMM methods, while numerical experiments demonstrate the computational benefits of the adaptive approach.
Recommended citation: Farias Maia, L., Gutman, D. H., Monteiro, R. D. C., & Silva, G. N. (2026). An adaptive proximal ADMM for nonconvex linearly constrained composite programs. Mathematical Programming. Advance online publication. https://doi.org/10.1007/s10107-026-02366-w