An Augmented Lagrangian Coordination-Decomposition Algorithm for Solving Distributed Non-Convex Programs

TL;DR

This paper introduces a new distributed algorithm combining augmented Lagrangian and block-coordinate descent techniques to efficiently solve non-convex programs with nonlinear couplings, with proven convergence to KKT points.

Contribution

It presents a novel two-layer decomposition algorithm that integrates multiplier methods with proximal BCD for non-convex distributed optimization.

Findings

Algorithm converges to a KKT point under semi-algebraicity.

Demonstrated effectiveness on a numerical example.

Combines augmented Lagrangian with block-coordinate descent in a distributed setting.

Abstract

A novel augmented Lagrangian method for solving non-convex programs with nonlinear cost and constraint couplings in a distributed framework is presented. The proposed decomposition algorithm is made of two layers: The outer level is a standard multiplier method with penalty on the nonlinear equality constraints, while the inner level consists of a block-coordinate descent (BCD) scheme. Based on standard results on multiplier methods and recent results on proximal regularised BCD techniques, it is proven that the method converges to a KKT point of the non-convex nonlinear program under a semi-algebraicity assumption. Efficacy of the algorithm is demonstrated on a numerical example.