New bounds for nonconvex quadratically constrained quadratic programming

نویسندگان

چکیده

Abstract In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of QCQPs, and cubic bounds. use affine functions as Lagrange multipliers demonstrate that most semidefinite relaxations can be obtained the dual a bound. addition, by changing ground set. For bounds, in addition to employ functions. provide comparison between proposed bound typical standard programs. Moreover, report results

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Hidden convexity in some nonconvex quadratically constrained quadratic programming

We consider the problem of minimizing an indefinite quadratic objective function subject to twosided indelinite quadratic constraints. Under a suitable simultaneous diagonalization assumption {which trivially holds for trust region type problems), we prove that the original problem is equivalent to a convex minimization problem with simple linear constraints. We then consider a special problem ...

متن کامل

Convex 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 کامل

Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems...

متن کامل

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 کامل

On 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 کامل

ذخیره 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: Journal of Global Optimization

سال: 2022

ISSN: ['1573-2916', '0925-5001']

DOI: https://doi.org/10.1007/s10898-022-01224-1