An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints

TL;DR

This paper introduces an inertial ADMM algorithm tailored for non-convex multi-block optimization problems with nonlinear coupling constraints, featuring novel update rules and proven convergence properties.

Contribution

It develops a new inertial ADMM method with unique update rules for primal and dual variables, ensuring convergence for complex non-convex problems.

Findings

Proposed method converges globally.

Inertial technique improves convergence speed.

Effective for non-convex problems with nonlinear constraints.

Abstract

In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method, when compared with other alternating direction methods of multipliers for solving non-convex problems with nonlinear coupling constraints, include: (i) we apply the inertial technique to the update of primal variables and (ii) we apply a non-standard update rule for the multiplier by scaling the multiplier by a factor before moving along the ascent direction where a relaxation parameter is allowed. Subsequential convergence and global convergence are presented for the proposed algorithm.