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.
Showing items related by title, author, creator and subject.
Liu, Chang (University of Waterloo, 2015-01-27)In today's competitive business environment, strategies relating to market forecasting, decision making and risk management have received a lot of attention. The empirical results reveal that the market movement is not ...
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 ...
Wang, Jian (University of Waterloo, 2010-04-19)Many optimal stochastic control problems in finance can be formulated in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). In this thesis, a general framework for solutions of HJB PDEs in ...