TY - JOUR
T1 - Distributed constrained optimization algorithms with linear convergence rate over time-varying unbalanced graphs
AU - Liu, Hongzhe
AU - Yu, Wenwu
AU - Zheng, Wei Xing
AU - Nedić, Angelia
AU - Zhu, Yanan
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2024/1
Y1 - 2024/1
N2 - 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.
AB - 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.
KW - Constrained convex optimization
KW - Distributed discrete-time algorithm
KW - Linear convergence rate
KW - Time-varying unbalanced graphs
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U2 - 10.1016/j.automatica.2023.111346
DO - 10.1016/j.automatica.2023.111346
M3 - Article
AN - SCOPUS:85174858567
SN - 0005-1098
VL - 159
JO - Automatica
JF - Automatica
M1 - 111346
ER -