Distributed constrained optimization algorithms with linear convergence rate over time-varying unbalanced graphs

Hongzhe Liu, Wenwu Yu, Wei Xing Zheng, Angelia Nedić, Yanan Zhu

Research output: Contribution to journalArticlepeer-review

Abstract

In this work, the constrained optimization problem is studied, where the global objective function is the sum of N convex functions and a closed convex set constraint is involved. The aim of this work is to design distributed optimization algorithms with linear convergence rate over time-varying unbalanced graphs for solving the studied problem. Towards this end, the Push-DIGing based accelerated distributed constrained optimization algorithm (PDADCO) and the Push-Pull based accelerated distributed constrained optimization algorithm (PPADCO) are developed. Specially, during the algorithm developments, the method of feasible direction, which can be successfully integrated into the Push-DIGing framework and the Push-Pull framework, is newly introduced to deal with the involved closed convex set constraint. Furthermore, based on the small gain theorem, the linear convergence properties of both the PDADCO and the PPADCO are rigorously established, with the feasible regions of the step-sizes being given. Finally, a simulation example is provided to verify the effectiveness of the established theoretical results.

Original languageEnglish (US)
Article number111346
JournalAutomatica
Volume159
DOIs
StatePublished - Jan 2024
Externally publishedYes

Keywords

  • Constrained convex optimization
  • Distributed discrete-time algorithm
  • Linear convergence rate
  • Time-varying unbalanced graphs

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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