On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming
MetadataShow full item record
Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength of Lagrangian Relaxation and the semidefinite relaxation. Then we focus on two special classes of QCQP, whose objective and constraint functions take the form trace(X^TQX + 2C^T X) + β, and trace(X^TQX + XPX^T + 2C^T X)+ β respectively, where X is an n by r real matrix. For each class of problems, we proposed different semidefinite relaxation formulations and compared their strength. The theoretical results obtained in this thesis have found interesting applications, e.g., solving the Quadratic Assignment Problem.
Cite this version of the work
Yichuan Ding (2007). On Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming. UWSpace. http://hdl.handle.net/10012/3044
Showing items related by title, author, creator and subject.
Alderson, Matthew (University of Waterloo, 2010-04-27)In recent years, the moments of L-functions has been a topic of growing interest in the field of analytic number theory. New techniques, including applications of Random Matrix Theory and multiple Dirichlet series, have ...
A Blueprint for Semidefinite Relaxations of Binary-Constrained Quadratic Programs Computing tight bounds on NP-hard problems using ADMM Graham, Naomi (University of Waterloo, 2020-12-18)This thesis looks at the solution techniques of two NP-hard, large scale problems, the quadratic assignment problem, QAP, and the side chain positioning, SCP, problem. We summarize existing approaches from and look at the ...
Feldmann, Adam (University of Waterloo, 2005)This thesis provides a survey of the attacks on multivariate cryptosystems. We begin by providing an outline of the general multivariate cryptosystem. Proceeding from there, we show that even with this level of detail, ...