Paper Info
Title
Faster, but weaker, relaxations for quadratically constrained quadratic programs
Abstract
We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order cone programming (SOCP) and, as a result, solve more quickly than SDP. A downside is that the calculated bounds are weaker than those gotten by SDP. The framework allows one to choose a block-diagonal structure for the mixed SOCP-SDP, which in turn allows one to control the speed and bound quality. For a fixed block-diagonal structure, we also introduce a procedure to improve the bound quality without increasing computation time significantly. The effectiveness of our framework is illustrated on a large sample of QCQPs from various sources.
Year
DOI
Venue
2014
10.1007/s10589-013-9618-8
Computational Optimization and Applications
Keywords
Field
DocType
Nonconvex quadratic programming,Semidefinite programming,Second-order cone programming,Difference of convex
Second-order cone programming,Quadratic growth,Mathematical optimization,Quadratically constrained quadratic program,Quadratic equation,Quadratic programming,Mathematics,Semidefinite programming,Computation
Journal
Volume
Issue
ISSN
59
1-2
0926-6003
Citations 
PageRank 
References 
4
0.41
14
Authors
3
Name
Order
Citations
PageRank
Samuel Burer150.77
S. Kim224814.25
Masakazu Kojima31603222.51