Linear Convergence of Distributed Aggregative Optimization with Coupled Inequality Constraints

TL;DR

This paper introduces a novel distributed primal-dual algorithm for aggregative optimization with coupled inequality constraints, demonstrating linear convergence and effectiveness through theoretical analysis and numerical validation.

Contribution

It is the first to address distributed aggregative optimization with coupled affine inequality constraints using a primal-dual approach.

Findings

Algorithm converges linearly to the optimal solution.

Theoretical analysis confirms convergence rate.

Numerical example validates the effectiveness of the method.

Abstract

This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all the agents' variables. To our best knowledge, this work is the first to address this problem, and a novel distributed aggregative primal-dual algorithm is proposed based on the dual diffusion strategy and gradient tracking technique. Through rigorous analysis, it is shown that the devised algorithm converges to the optimal solution at a linear rate. Finally, a numerical example is conducted to illustrate the effectiveness of the theoretical results.