Momentum-based distributed gradient tracking algorithms for distributed aggregative optimization over unbalanced directed graphs

This paper studies a distributed aggregative optimization problem over a directed graph with the row-stochastic weighted matrix. Different from the existing work on distributed optimization, the local cost function of each agent depends both on its local decision variable and on the sum of all funct...

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Veröffentlicht in:Automatica (Oxford) Jg. 164; S. 111596
Hauptverfasser: Wang, Zhu, Wang, Dong, Lian, Jie, Ge, Hongwei, Wang, Wei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.06.2024
Schlagworte:
Acceleration
Distributed aggregative optimization
Gradient tracking
Linear convergence
Row-stochastic weighted matrix
Row-stochastic weighted matrix
Gradient tracking
Distributed aggregative optimization
Linear convergence
Acceleration
ISSN:0005-1098, 1873-2836
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Beschreibung
Zusammenfassung:This paper studies a distributed aggregative optimization problem over a directed graph with the row-stochastic weighted matrix. Different from the existing work on distributed optimization, the local cost function of each agent depends both on its local decision variable and on the sum of all functions formed by the decision variables of all agents. Inspired by the distributed dynamic average consensus protocol, heavy-ball strategy, and Nesterov gradient descent method, a momentum-based distributed gradient tracking algorithm with a fixed step size is proposed to solve such a problem. Further, it is shown that the proposed algorithm has a linear convergence rate if the global cost function is strongly convex with the Lipschitz-continuous gradient. The upper bounds of the fixed step size and the momentum parameter are restricted by a sufficiently small positive constant, respectively. Finally, a numerical example is provided to verify the effectiveness of the findings.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2024.111596