A bilinear formulation for vector sparsity optimization
Signal Processing
Optimal beamforming for two-way multi-antenna relay channel with analogue network coding
IEEE Journal on Selected Areas in Communications - Special issue on network coding for wireless communication networks
On capacity region of two-way multi-antenna relay channel with analogue network coding
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Journal of Global Optimization
Semidefinite relaxation bounds for bi-quadratic optimization problems with quadratic constraints
Journal of Global Optimization
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
Eigenvalue techniques for convex objective, nonconvex optimization problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Maximum Block Improvement and Polynomial Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint
Journal of Global Optimization
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In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed on the case in which the constraints are two quadratic inequalities. This formulation is termed the extended trust region subproblem in this paper, to distinguish it from the ordinary trust region subproblem, in which the constraint is a single ellipsoid. The computational complexity of the extended trust region subproblem in general is still unknown. In this paper we consider several interesting cases related to this problem and show that for those cases the corresponding semidefinite programming relaxation admits no gap with the true optimal value, and consequently we obtain polynomial-time procedures for solving those special cases of quadratic optimization. For the extended trust region subproblem itself, we introduce a parameterized problem and prove the existence of a trajectory that will lead to an optimal solution. Combining this with a result obtained in the first part of the paper, we propose a polynomial-time solution procedure for the extended trust region subproblem arising from solving nonlinear programs with a single equality constraint.