Fast ADMM for Semidefinite Programs with Chordal Sparsity
File(s)
Accepted version
Author(s)
Zheng, Yang
Fantuzzi, Giovanni
Papachristodoulou, Antonis
Goulart, Paul
Wynn, Andrew
Type
Conference Paper
Abstract
Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve SDPs with chordal sparsity based on the alternating direction method of multipliers (ADMM). We show that chordal decomposition can be applied to either the primal or the dual standard form of a sparse SDP, resulting in scaled versions of ADMM algorithms with the same computational cost. Each iteration of our algorithms consists of a projection on the product of small positive semidefinite cones, followed by a projection on an affine set, both of which can be carried out efficiently. Our techniques are implemented in CDCS, an open source add-on to MATLAB. Numerical experiments on large-scale sparse problems in SDPLIB and random SDPs with block-arrow sparse patterns show speedups compared to some common state-of-the-art software packages.
Date Issued
2017-07-03
Date Acceptance
2017-01-22
Citation
2017
Publisher
IEEE
Copyright Statement
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Identifier
http://arxiv.org/abs/1609.06068v3
Source
2017 American Control Conference
Subjects
math.OC
math.OC
Notes
6 pages. Codes available from http://github.com/giofantuzzi/CDCS . Accepted in the American Control Conference, 2017 http://ieeexplore.ieee.org/abstract/document/7963462/
Start Date
2017-05-24
Finish Date
2017-05-26
Coverage Spatial
Sheraton Seattle Hotel, Seattle, WA, USA
Date Publish Online
2017-07-03