On convex relaxations for quadratically constrained quadratic programming
نویسندگان
چکیده
منابع مشابه
On convex relaxations for quadratically constrained quadratic programming
We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint functions with their convex lower envelopes on F is dominated by an alternative methodology based ...
متن کاملOn Efficient Semidefinite Relaxations for Quadratically Constrained Quadratic Programming
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 semi...
متن کاملConvex quadratic relaxations of nonconvex quadratically constrained quadratic programs
Nonconvex quadratic constraints can be linearized to obtain relaxations in a wellunderstood manner. We propose to tighten the relaxation by using second order cone constraints, resulting in a convex quadratic relaxation. Our quadratic approximation to the bilinear term is compared to the linear McCormick bounds. The second order cone constraints are based on linear combinations of pairs of vari...
متن کاملLinear Programming Relaxations of Quadratically Constrained Quadratic Programs
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and principal minors PSD cuts. Computational results based on instances from the literature are presented.
متن کاملFaster, but weaker, relaxations for quadratically constrained quadratic programs
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 SD...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2012
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-012-0602-3