Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

TL;DR

This paper derives convergence rate bounds for a proximal ADMM variant with an over-relaxation parameter in (0,2) for nonconvex linearly constrained problems, extending previous work limited to smaller parameter ranges.

Contribution

It introduces convergence bounds for a proximal ADMM with an over-relaxation parameter in (0,2), broadening the parameter range considered in nonconvex optimization.

Findings

Established convergence rate bounds for the proposed method.

Extended the over-relaxation parameter range beyond previous limits.

Provided theoretical guarantees for nonconvex constrained problems.

Abstract

This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval $(0,2)$. To the best of our knowledge, all related papers in the literature only consider the case where the over-relaxation parameter lies in the interval $(0,(1+\sqrt{5})/2)$.