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Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint |
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| Authors: | Harish J. Palanthandalam-Madapusi Tobin H. Van Pelt Dennis S. Bernstein |
| Affiliation: | (1) Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia;(2) Present address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, 3353, VIC, Australia;(3) Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China |
| Abstract: | We consider minimization of a quadratic objective function subject to a sign-indefinite quadratic equality constraint. We derive necessary and sufficient conditions for the existence of solutions to the constrained minimization problem. These conditions involve a generalized eigenvalue of the matrix pencil consisting of a symmetric positive-semidefinite matrix and a symmetric indefinite matrix. A complete characterization of the solution set to the constrained minimization problem in terms of the eigenspace of the matrix pencil is provided. |
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