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82
Semidefinite . . . Technique for Nonconvex Quadratically Constrained Quadratic Programming
, 2007
"... We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial por ..."
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We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial
Semidefinite relaxation of quadratic optimization problems
 SIGNAL PROCESSING MAGAZINE, IEEE
, 2010
"... n recent years, the semidefinite relaxation (SDR) technique has been at the center of some of very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, computa ..."
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Cited by 161 (11 self)
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, computationally efficient approximation technique for a host of very difficult optimization problems. In particular, it can be applied to many nonconvex quadratically constrained quadratic programs (QCQPs) in an almost mechanical fashion, including the following problem: min x[Rn x T
Approximation bounds for quadratic optimization with homogeneous quadratic constraints
 SIAM J. Optim
, 2007
"... Abstract. We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program ..."
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Cited by 49 (24 self)
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Abstract. We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic
SemidefiniteBased BranchandBound for Nonconvex Quadratic Programming
, 2005
"... This paper presents a branchandbound algorithm for nonconvex quadratic programming, which is based on solving semidefinite relaxations at each node of the enumeration tree. The method is motivated by a recent branchandcut approach for the boxconstrained case that employs linear relaxations of t ..."
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This paper presents a branchandbound algorithm for nonconvex quadratic programming, which is based on solving semidefinite relaxations at each node of the enumeration tree. The method is motivated by a recent branchandcut approach for the boxconstrained case that employs linear relaxations
Approximation Bounds for Quadratic Maximization with Semidefinite Programming Relaxation
, 2003
"... In this paper, we consider a class of quadratic maximization problems. One important instance in that class is the famous quadratic maximization formulation of the maxcut problem studied by Goemans and Williamson [6]. Since the problem is NPhard in general, following Goemans and Williamson, we app ..."
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Cited by 3 (0 self)
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apply the approximation method based on the semidefinite programming (SDP) relaxation. For a subclass of the problems, including the ones studied by Helmberg [9] and Zhang [23], we show that the SDP relaxation approach yields an approximation solution with the worstcase performance ratio at least alpha
Semidefinite programming versus the reformulationlinearization technique for nonconvex quadratically constrained quadratic programming
, 2007
"... We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial por ..."
Abstract

Cited by 28 (5 self)
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We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulationlinearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial
Approximation Bounds for Quadratic Optimization with Homogeneous Quadratic Constraints∗
, 2006
"... We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) pr ..."
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We consider the NPhard problem of finding a minimum norm vector in ndimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP
On convex relaxations for quadratically constrained quadratic programming
 Mathematical Programming (Series B
, 2012
"... 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 f ..."
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Cited by 14 (0 self)
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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
An LPCC Approach to Nonconvex Quadratic Programs
, 2008
"... Filling a gap in nonconvex quadratic programming, this paper shows that the global resolution of a feasible quadratic program (QP), which is not known a priori to be bounded or unbounded below, can be accomplished in finite time by solving a linear program with linear complementarity constraints, i. ..."
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Cited by 6 (2 self)
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Filling a gap in nonconvex quadratic programming, this paper shows that the global resolution of a feasible quadratic program (QP), which is not known a priori to be bounded or unbounded below, can be accomplished in finite time by solving a linear program with linear complementarity constraints, i
Improved Approximation Bound for Quadratic Optimization Problems with Orthogonality Constraints
 In Proceedings of the ACMSIAM Symposium on Discrete Algorithms (SODA
, 2009
"... In this paper we consider the problem of approximating a class of quadratic optimization problems that contain orthogonality constraints, i.e. constraints of the form X T X = I, where X ∈ R m×n is the optimization variable. This class of problems, which we denote by (Qp–Oc), is quite general and cap ..."
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Cited by 7 (0 self)
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In this paper we consider the problem of approximating a class of quadratic optimization problems that contain orthogonality constraints, i.e. constraints of the form X T X = I, where X ∈ R m×n is the optimization variable. This class of problems, which we denote by (Qp–Oc), is quite general
Results 1  10
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82