A Distributed Gradient-based Algorithm for Optimization Problems with Coupled Equality Constraints

TL;DR

This paper introduces a fully distributed gradient-based optimization algorithm for coupled equality constraints that avoids complex local subproblem solving, ensuring efficiency and scalability in networked systems.

Contribution

The paper presents a novel distributed gradient method that bypasses local argmin computations, with proven convergence properties and demonstrated superior performance.

Findings

Achieves sublinear convergence for convex functions.

Attains linear convergence under strong convexity and smoothness.

Shows improved efficiency and scalability in numerical simulations.

Abstract

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each iteration. Such approaches become computationally burdensome or intractable when local cost functions are complex. To address this challenge, we propose a novel distributed gradient-based algorithm that avoids solving a local optimization problem at each iteration by leveraging first-order approximations and projection onto local feasible sets. The algorithm operates in a fully distributed manner, requiring only local communication without exchanging gradients or primal variables. We rigorously establish sublinear convergence for general convex cost functions and linear convergence under strong convexity and smoothness conditions. Numerical simulation on the IEEE 118-bus system demonstrates the superior computational efficiency and scalability of the proposed method compared to several state-of-the-art distributed optimization algorithms.