TY - GEN
T1 - A fast distributed algorithm for decomposable semidefinite programs
AU - Kalbat, Abdulrahman
AU - Lavaei, Javad
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84962019382&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84962019382&partnerID=8YFLogxK
U2 - 10.1109/CDC.2015.7402462
DO - 10.1109/CDC.2015.7402462
M3 - Conference contribution
AN - SCOPUS:84962019382
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1742
EP - 1749
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -