Global minimization of large-scale constrained concave quadratic problems by separable programming
Mathematical Programming: Series A and B
Constrained global optimization: algorithms and applications
Constrained global optimization: algorithms and applications
An algorithm for global minimization of linearly constrained concave quadratic functions
Mathematics of Operations Research
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
SIAM Review
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs
Journal of Global Optimization
Approximating Global Quadratic Optimization with Convex Quadratic Constraints
Journal of Global Optimization
On Copositive Programming and Standard Quadratic Optimization Problems
Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
Enhancing RLT relaxations via a new class of semidefinite cuts
Journal of Global Optimization
An algorithmic analysis of multiquadratic and semidefinite programming problems
An algorithmic analysis of multiquadratic and semidefinite programming problems
Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations
Computational Optimization and Applications
Computational Optimization and Applications
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs
Mathematical Programming: Series A and B
D.C. Versus Copositive Bounds for Standard QP
Journal of Global Optimization
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We propose in this paper a general D.C. decomposition scheme for constructing SDP relaxation formulations for a class of nonconvex quadratic programs with a nonconvex quadratic objective function and convex quadratic constraints. More specifically, we use rank-one matrices and constraint matrices to decompose the indefinite quadratic objective into a D.C. form and underestimate the concave terms in the D.C. decomposition formulation in order to get a convex relaxation of the original problem. We show that the best D.C. decomposition can be identified by solving an SDP problem. By suitably choosing the rank-one matrices and the linear underestimation, we are able to construct convex relaxations that dominate Shor's SDP relaxation and the strengthened SDP relaxation. We then propose an extension of the D.C. decomposition to generate an SDP bound that is tighter than the SDP+RLT bound when additional box constraints are present. We demonstrate via computational results that the optimal D.C. decomposition schemes can generate both tight SDP bounds and feasible solutions with good approximation ratio for nonconvex quadratically constrained quadratic problems.