A forward-backward algorithm for decomposable semi-definite programs

Filippo Fabiani; Sergio Grammatico

doi:10.1109/MED48518.2020.9182860

A forward-backward algorithm for decomposable semi-definite programs

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

Abstract

We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semi-definite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost, numerically comparing their performances with respect to others available in the literature.

Original language	English
Title of host publication	Proceedings of the 28th Mediterranean Conference on Control and Automation, MED 2020
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	580-585
ISBN (Electronic)	978-1-7281-5742-9
DOIs	https://doi.org/10.1109/MED48518.2020.9182860
Publication status	Published - 2020
Event	28th Mediterranean Conference on Control and Automation, MED 2020 - Saint-Raphael, France Duration: 15 Sept 2020 → 18 Sept 2020

Conference

Conference	28th Mediterranean Conference on Control and Automation, MED 2020
Country/Territory	France
City	Saint-Raphael
Period	15/09/20 → 18/09/20

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10.1109/MED48518.2020.9182860

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title = "A forward-backward algorithm for decomposable semi-definite programs",

abstract = "We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semi-definite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost, numerically comparing their performances with respect to others available in the literature.",

author = "Filippo Fabiani and Sergio Grammatico",

year = "2020",

doi = "10.1109/MED48518.2020.9182860",

language = "English",

pages = "580--585",

booktitle = "Proceedings of the 28th Mediterranean Conference on Control and Automation, MED 2020",

publisher = "IEEE",

address = "United States",

note = "28th Mediterranean Conference on Control and Automation, MED 2020 ; Conference date: 15-09-2020 Through 18-09-2020",

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Fabiani, F & Grammatico, S 2020, A forward-backward algorithm for decomposable semi-definite programs. in Proceedings of the 28th Mediterranean Conference on Control and Automation, MED 2020. IEEE, Piscataway, NJ, USA, pp. 580-585, 28th Mediterranean Conference on Control and Automation, MED 2020, Saint-Raphael, France, 15/09/20. https://doi.org/10.1109/MED48518.2020.9182860

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AU - Fabiani, Filippo

AU - Grammatico, Sergio

PY - 2020

Y1 - 2020

N2 - We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semi-definite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost, numerically comparing their performances with respect to others available in the literature.

AB - We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semi-definite programs (SDPs). We exploit a chordal aggregate sparsity pattern assumption on the original SDP to obtain a set of mutually coupled SDPs defined on positive semidefinite (PSD) cones of reduced dimensions. We show that the proposed algorithms converge to a solution of the original SDP via iterations of reasonable computational cost, numerically comparing their performances with respect to others available in the literature.

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U2 - 10.1109/MED48518.2020.9182860

DO - 10.1109/MED48518.2020.9182860

M3 - Conference contribution

AN - SCOPUS:85092194286

SP - 580

EP - 585

BT - Proceedings of the 28th Mediterranean Conference on Control and Automation, MED 2020

PB - IEEE

CY - Piscataway, NJ, USA

T2 - 28th Mediterranean Conference on Control and Automation, MED 2020

Y2 - 15 September 2020 through 18 September 2020

ER -

A forward-backward algorithm for decomposable semi-definite programs

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