Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
A p-cone sequential relaxation procedure for 0-1 integer programs
Optimization Methods & Software - GLOBAL OPTIMIZATION
Journal of Global Optimization
Second-Order Cone Relaxations for Binary Quadratic Polynomial Programs
SIAM Journal on Optimization
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
A quasi-linear algorithm for calculating the infimal convolution of convex quadratic functions
Journal of Computational and Applied Mathematics
On solving biquadratic optimization via semidefinite relaxation
Computational Optimization and Applications
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We show that SDP (semidefinite programming) and SOCP (second order cone programming) relaxations provide exact optimal solutions for a class of nonconvex quadratic optimization problems. It is a generalization of the results by S. Zhang for a subclass of quadratic maximization problems that have nonnegative off-diagonal coefficient matrices of quadratic objective functions and diagonal coefficient matrices of quadratic constraint functions. A new SOCP relaxation is proposed for the class of nonconvex quadratic optimization problems by extracting valid quadratic inequalities for positive semidefinite cones. Its effectiveness to obtain optimal values is shown to be the same as the SDP relaxation theoretically. Numerical results are presented to demonstrate that the SOCP relaxation is much more efficient than the SDP relaxation.