期刊
SIAM JOURNAL ON OPTIMIZATION
卷 17, 期 3, 页码 844-860出版社
SIAM PUBLICATIONS
DOI: 10.1137/050644471
关键词
quadratic programming; nonconvex optimization; strong duality; quadratic mappings
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.
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