A Distributed Nesterov-Like Gradient Tracking Algorithm for Composite Constrained Optimization

This paper focuses on the constrained optimization problem where the objective function is composed of smooth (possibly nonconvex) and nonsmooth parts. The proposed algorithm integrates the successive convex approximation (SCA) technique with the gradient tracking mechanism that aims at achieving a...

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Bibliographic Details
Published in:IEEE transactions on signal and information processing over networks Vol. 9; pp. 1 - 13
Main Authors: Zheng, Lifeng, Li, Huaqing, Li, Jun, Wang, Zheng, Lu, Qingguo, Shi, Yawei, Wang, Huiwei, Dong, Tao, Ji, Lianghao, Xia, Dawen
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Convergence
Distributed algorithms
distributed optimization
gradient tracking
Information processing
Linear programming
Manganese
Momentum
Nesterov method
nonconvex optimization
Optimization
Successive convex approximation (SCA)
Tracking
Upper bounds
ISSN:2373-776X, 2373-7778
Online Access:Get full text
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Summary:This paper focuses on the constrained optimization problem where the objective function is composed of smooth (possibly nonconvex) and nonsmooth parts. The proposed algorithm integrates the successive convex approximation (SCA) technique with the gradient tracking mechanism that aims at achieving a linear convergence rate and employing the momentum term to regulate update directions in each time instant. It is proved that the proposed algorithm converges provided that the constant step size and momentum parameter are lower than the given upper bounds. When the smooth part is strongly convex, the proposed algorithm linearly converges to the global optimal solution, whereas it converges to a local stationary solution with a sub-linear convergence rate if the smooth part is nonconvex. Numerical simulations are applied to demonstrate the validity of the proposed algorithm and the theoretical analysis.
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ISSN:2373-776X
2373-7778
DOI:10.1109/TSIPN.2023.3239698