Bregman Parallel Direction Method of Multipliers for Distributed Optimization via Mirror Averaging

Yue Yu; Behcet Acikmese; Mehran Mesbahi

doi:10.1109/LCSYS.2018.2833116

Bregman Parallel Direction Method of Multipliers for Distributed Optimization via Mirror Averaging

Yue Yu, Behcet Acikmese, Mehran Mesbahi

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and O(1/T) convergence rate of the Bregman PDMM, along with its O(n/n) improvement over existing PDMM, where T denotes the number of iterations and n the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.

Original language	English (US)
Pages (from-to)	302-306
Number of pages	5
Journal	IEEE Control Systems Letters
Volume	2
Issue number	2
DOIs	https://doi.org/10.1109/LCSYS.2018.2833116
State	Published - Apr 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

Optimization algorithms
distributed control
distributed optimization

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10.1109/LCSYS.2018.2833116

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abstract = "Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and O(1/T) convergence rate of the Bregman PDMM, along with its O(n/n) improvement over existing PDMM, where T denotes the number of iterations and n the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.",

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author = "Yue Yu and Behcet Acikmese and Mehran Mesbahi",

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AU - Acikmese, Behcet

AU - Mesbahi, Mehran

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Y1 - 2018/4

N2 - Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and O(1/T) convergence rate of the Bregman PDMM, along with its O(n/n) improvement over existing PDMM, where T denotes the number of iterations and n the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.

AB - Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and O(1/T) convergence rate of the Bregman PDMM, along with its O(n/n) improvement over existing PDMM, where T denotes the number of iterations and n the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.

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Bregman Parallel Direction Method of Multipliers for Distributed Optimization via Mirror Averaging

Abstract

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