Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound
Foundations and Trends in Signal Processing
Robust linear MIMO in the downlink: a worst-case optimization with ellipsoidal uncertainty regions
EURASIP Journal on Advances in Signal Processing
IEEE Transactions on Communications
Robust collaborative-relay beamforming
IEEE Transactions on Signal Processing
Adaptive detection and estimation in the presence of useful signal and interference mismatches
IEEE Transactions on Signal Processing
Robust cognitive beamforming with bounded channel uncertainties
IEEE Transactions on Signal Processing
Journal of Global Optimization
Structured Total Maximum Likelihood: An Alternative to Structured Total Least Squares
SIAM Journal on Matrix Analysis and Applications
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
Journal of Global Optimization
SDP reformulation for robust optimization problems based on nonconvex QP duality
Computational Optimization and Applications
Wireless Personal Communications: An International Journal
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We consider the problem of minimizing an indefinite quadratic function subject to two quadratic inequality constraints. When the problem is defined over the complex plane we show that strong duality holds and obtain necessary and sufficient optimality conditions. We then develop a connection between the image of the real and complex spaces under a quadratic mapping, which together with the results in the complex case lead to a condition that ensures strong duality in the real setting. Preliminary numerical simulations suggest that for random instances of the extended trust region subproblem, the sufficient condition is satisfied with a high probability. Furthermore, we show that the sufficient condition is always satisfied in two classes of nonconvex quadratic problems. Finally, we discuss an application of our results to robust least squares problems.