Extended Zero-Gradient-Sum Approach for Constrained Distributed Optimization with Free Initialization

TL;DR

This paper introduces an extended zero-gradient-sum approach with a Newton-based continuous-time algorithm for constrained distributed optimization, achieving various convergence rates and handling inequality constraints effectively.

Contribution

It extends the EZGS method to constrained distributed optimization with free initialization, incorporating heterogeneous power coefficients and a barrier method for inequalities.

Findings

Achieves exponential, finite, fixed, and prescribed-time convergence.

Handles inequality constraints using barrier methods.

Validated by numerical examples demonstrating effectiveness.

Abstract

This paper proposes an extended zero-gradient-sum (EZGS) approach for solving constrained distributed optimization (DO) with free initialization. A Newton-based continuous-time algorithm (CTA) is first designed for general constrained optimization and then extended to solve constrained DO based on the EZGS method. It is shown that for typical consensus protocols, the EZGS CTA can achieve the performance with exponential/finite/fixed/prescribed-time convergence. Particularly, the nonlinear consensus protocols for finite-time EZGS algorithms can have heterogeneous power coefficients. The prescribed-time EZGS dynamics is continuous and uniformly bounded, which can achieve the optimal solution in one stage. Moreover, the barrier method is employed to tackle the inequality constraints. Finally, the performance of the proposed algorithms is verified by numerical examples.