Distributed Optimization with Coupling Constraints

TL;DR

This paper introduces IPLUX, a novel distributed primal-dual algorithm for convex optimization with complex coupled constraints, achieving faster convergence and practical efficiency.

Contribution

The paper develops a new integrated primal-dual proximal algorithm for distributed convex optimization with coupled nonlinear and linear constraints, improving convergence rates.

Findings

Achieves an $O(1/k)$ convergence rate in optimality and feasibility.

Outperforms existing algorithms in convergence speed.

Demonstrates competitive practical performance in simulations.

Abstract

In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be fully coupled. Specifically, we first separate the constraints into three groups, and design two primal-dual methods and utilize a virtual-queue-based method to handle each group of the constraints independently. Then, we integrate these three methods in a strategic way, leading to an integrated primal-dual proximal (IPLUX) algorithm, and enable the distributed implementation of IPLUX. We show that IPLUX achieves an $O(1/k)$ rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the state-of-the-art distributed algorithms for convex optimization with coupling nonlinear constraints. Finally, IPLUX exhibits competitive practical performance in the simulations.