On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers

Guoqiang Zhang; Matthew Orconnor; Le Li

doi:10.1109/SSP.2018.8450854

On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers

Guoqiang Zhang, Matthew Orconnor, Le Li

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

Recently, the primal-dual method of multipliers (PDMM) has been proposed and successfully applied to solve a number of decomposable convex optimizations distributedly and iteratively. In this work, we study the gradient based PDMM (GPDMM), where the objective functions are approximated using the gradient information per iteration. It is shown that for a certain class of decomposable convex optimizations, synchronous GPDMM has a sublinear convergence rate of O(1/K) (where K denotes the iteration index). Experiments on a problem of distributed ridge regularized logistic regression demonstrate the efficiency of synchronous GPDMM.

Original language	English
Title of host publication	2018 IEEE Statistical Signal Processing Workshop, SSP 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	353-357
Number of pages	5
ISBN (Print)	9781538615706
DOIs	https://doi.org/10.1109/SSP.2018.8450854
Publication status	Published - 29 Aug 2018
Event	20th IEEE Statistical Signal Processing Workshop, SSP 2018 - Freiburg im Breisgau, Germany Duration: 10 Jun 2018 → 13 Jun 2018

Publication series

Name	2018 IEEE Statistical Signal Processing Workshop, SSP 2018

Conference

Conference	20th IEEE Statistical Signal Processing Workshop, SSP 2018
Country/Territory	Germany
City	Freiburg im Breisgau
Period	10/06/18 → 13/06/18

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10.1109/SSP.2018.8450854

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Zhang, G., Orconnor, M., & Li, L. (2018). On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers. In 2018 IEEE Statistical Signal Processing Workshop, SSP 2018 (pp. 353-357). Article 8450854 (2018 IEEE Statistical Signal Processing Workshop, SSP 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SSP.2018.8450854

@inproceedings{595080ff56ca40659b810bf989d20d32,

title = "On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers",

abstract = "Recently, the primal-dual method of multipliers (PDMM) has been proposed and successfully applied to solve a number of decomposable convex optimizations distributedly and iteratively. In this work, we study the gradient based PDMM (GPDMM), where the objective functions are approximated using the gradient information per iteration. It is shown that for a certain class of decomposable convex optimizations, synchronous GPDMM has a sublinear convergence rate of O(1/K) (where K denotes the iteration index). Experiments on a problem of distributed ridge regularized logistic regression demonstrate the efficiency of synchronous GPDMM.",

keywords = "ADMM, Distributed optimization, PDMM, convergence analysis",

author = "Guoqiang Zhang and Matthew Orconnor and Le Li",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 20th IEEE Statistical Signal Processing Workshop, SSP 2018 ; Conference date: 10-06-2018 Through 13-06-2018",

year = "2018",

month = aug,

day = "29",

doi = "10.1109/SSP.2018.8450854",

language = "English",

isbn = "9781538615706",

series = "2018 IEEE Statistical Signal Processing Workshop, SSP 2018",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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}

Zhang, G, Orconnor, M & Li, L 2018, On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers. in 2018 IEEE Statistical Signal Processing Workshop, SSP 2018., 8450854, 2018 IEEE Statistical Signal Processing Workshop, SSP 2018, Institute of Electrical and Electronics Engineers Inc., pp. 353-357, 20th IEEE Statistical Signal Processing Workshop, SSP 2018, Freiburg im Breisgau, Germany, 10/06/18. https://doi.org/10.1109/SSP.2018.8450854

On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers. / Zhang, Guoqiang; Orconnor, Matthew; Li, Le.
2018 IEEE Statistical Signal Processing Workshop, SSP 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 353-357 8450854 (2018 IEEE Statistical Signal Processing Workshop, SSP 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers

AU - Zhang, Guoqiang

AU - Orconnor, Matthew

AU - Li, Le

PY - 2018/8/29

Y1 - 2018/8/29

N2 - Recently, the primal-dual method of multipliers (PDMM) has been proposed and successfully applied to solve a number of decomposable convex optimizations distributedly and iteratively. In this work, we study the gradient based PDMM (GPDMM), where the objective functions are approximated using the gradient information per iteration. It is shown that for a certain class of decomposable convex optimizations, synchronous GPDMM has a sublinear convergence rate of O(1/K) (where K denotes the iteration index). Experiments on a problem of distributed ridge regularized logistic regression demonstrate the efficiency of synchronous GPDMM.

AB - Recently, the primal-dual method of multipliers (PDMM) has been proposed and successfully applied to solve a number of decomposable convex optimizations distributedly and iteratively. In this work, we study the gradient based PDMM (GPDMM), where the objective functions are approximated using the gradient information per iteration. It is shown that for a certain class of decomposable convex optimizations, synchronous GPDMM has a sublinear convergence rate of O(1/K) (where K denotes the iteration index). Experiments on a problem of distributed ridge regularized logistic regression demonstrate the efficiency of synchronous GPDMM.

KW - ADMM

KW - Distributed optimization

KW - PDMM

KW - convergence analysis

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U2 - 10.1109/SSP.2018.8450854

DO - 10.1109/SSP.2018.8450854

M3 - Conference contribution

SN - 9781538615706

T3 - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

SP - 353

EP - 357

BT - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 20th IEEE Statistical Signal Processing Workshop, SSP 2018

Y2 - 10 June 2018 through 13 June 2018

ER -

On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers

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