A fast distributed algorithm for decomposable semidefinite programs

Abdulrahman Kalbat, Javad Lavaei

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

Abstract

This paper aims to develop a fast, parallelizable algorithm for an arbitrary decomposable semidefinite program (SDP). To formulate a decomposable SDP, we consider a multi-agent canonical form represented by a graph, where each agent (node) is in charge of computing its corresponding positive semidefinite matrix subject to local equality and inequality constraints as well as overlapping (consistency) constraints with regards to the agent's neighbors. Based on the alternating direction method of multipliers, we design a numerical algorithm, which has a guaranteed convergence under very mild assumptions. Each iteration of this algorithm has a simple closed-form solution, consisting of matrix multiplications and eigenvalue decompositions performed by individual agents as well as information exchanges between neighboring agents. The cheap iterations of the proposed algorithm enable solving real-world large-scale conic optimization problems.

Original languageEnglish
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1742-1749
Number of pages8
ISBN (Electronic)9781479978861
DOIs
Publication statusPublished - Feb 8 2015
Externally publishedYes
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference54th IEEE Conference on Decision and Control, CDC 2015
Country/TerritoryJapan
CityOsaka
Period12/15/1512/18/15

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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