Paper Info
Title
Local Minima and Convergence in Low-Rank Semidefinite Programming
Abstract
The low-rank semidefinite programming problem LRSDPr is a restriction of the semidefinite programming problem SDP in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr and prove the optimal convergence of a slight variant of the successful, yet experimental, algorithm of Burer and Monteiro [5], which handles LRSDPr via the nonconvex change of variables X=RRT. In addition, for particular problem classes, we describe a practical technique for obtaining lower bounds on the optimal solution value during the execution of the algorithm. Computational results are presented on a set of combinatorial optimization relaxations, including some of the largest quadratic assignment SDPs solved to date.
Year
DOI
Venue
2005
10.1007/s10107-004-0564-1
Math. Program.
Keywords
Field
DocType
semideflnite programming,largest quadratic assignment,low-rank semidefinite programming problem,bound r,nonlinear programming,combinatorial optimization relaxation,local minima,augmented lagrangian,combinatorial optimization,numerical experiments.,low-rank matrices,variables x,computational result,vector programming,particular problem class,low-rank semidefinite programming,optimal convergence,optimal solution value,semidefinite programming problem sdp,lower bound,semidefinite programming
Change of variables,Discrete mathematics,Mathematical optimization,Nonlinear programming,Quadratic equation,Combinatorial optimization,Maxima and minima,Augmented Lagrangian method,Semidefinite embedding,Mathematics,Semidefinite programming
Journal
Volume
Issue
ISSN
103
3
1436-4646
Citations 
PageRank 
References 
100
8.02
17
Authors
2
Name
Order
Citations
PageRank
Samuel Burer1114873.09
Renato D. C. Monteiro21250138.18