Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints

TL;DR

This paper introduces a multiblock ADMM algorithm for complex nonsmooth, nonconvex optimization problems with nonlinear constraints, proving convergence and demonstrating preliminary numerical effectiveness.

Contribution

It develops a novel multiblock ADMM method incorporating majorization minimization for nonconvex problems with nonlinear coupling, with proven convergence and complexity analysis.

Findings

Proves subsequential and global convergence to critical points.

Establishes iteration complexity bounds.

Provides preliminary numerical results demonstrating effectiveness.

Abstract

This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in the update of each block of the primal variables. Subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian are proved. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.