Distributed Optimization With Coupling Constraints

In this article, we investigate distributed convex opti-mization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely cou-pling. By strategically integrating ideas from primal-dual, proxi-mal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the prob-lem over a connected, undirected graph. 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 alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation.

Automated summary

In this article, the authors investigate distributed convex optimization with both inequality and equality constraints. They propose a novel distributed algorithm called IPLUX, which integrates ideas from primal-dual, proximal, and virtual-queue optimization methods. The algorithm achieves an O(1/k) rate of convergence in terms of optimality and feasibility, outperforming alternative methods and eliminating the assumption on the compactness of the feasible region. Simulation results demonstrate that IPLUX exhibits faster convergence and higher efficiency compared to state-of-the-art methods.