Peng, Ji-Ming; Yuan, Ya-xiang Optimality conditions for the minimization of a quadratic with two quadratic constraints. (English) Zbl 0891.90150 SIAM J. Optim. 7, No. 3, 579-594 (1997). Summary: The trust region method has been proven to be very successful in both unconstrained and constrained optimization. It requires the global minimum of a general quadratic function subject to ellipsoid constraints. In this paper, we generalize the trust region subproblem by allowing two general quadratic constraints. Conditions and properties of its solution are discussed. Cited in 49 Documents MSC: 90C30 Nonlinear programming Keywords:trust region method; global minimizer; constrained optimization; subproblem; quadratic constraint Software:GQTPAR PDFBibTeX XMLCite \textit{J.-M. Peng} and \textit{Y.-x. Yuan}, SIAM J. Optim. 7, No. 3, 579--594 (1997; Zbl 0891.90150) Full Text: DOI