Paper Info
Title
Sparse Semidefinite Programs With Near-Linear Time Complexity
Abstract
Some of the strongest polynomial-time relaxations to NP-hard combinatorial optimization problems are semidefinite programs (SDPs), but their solution complexity of up to O(n (6.5) L) time and O(n(4)) memory for L accurate digits limits their use in all but the smallest problems. Given that combinatorial SDP relaxations are often sparse, a technique known as chordal conversion can sometimes reduce complexity substantially. In this paper, we describe a modification of chordal conversion that allows any general-purpose interiorpoint method to solve a certain class of sparse SDPs with a guaranteed complexity of O(n(1.5) L) time and O(n) memory. To illustrate the use of this technique, we solve the MAX k-CUT relaxation and the Lovasz Theta problem on power system models with up to n = 13659 nodes in 5 minutes, using SeDuMi v1.32 on a 1.7 GHz CPU with 16 GB of RAM. The empirical time complexity for attaining L decimal digits of accuracy is approximate to 0.001n (1.1) L seconds.
Year
DOI
Venue
2018
10.1109/CDC.2018.8619478
2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC)
Field
DocType
ISSN
Sparse approximation,Algorithm,Time complexity,Semidefinite embedding,Mathematics
Conference
0743-1546
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Richard Y. Zhang1106.92
Javad Lavaei258771.90