Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint

Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint

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Article ID: iaor200971831
Country: Netherlands
Volume: 45
Issue: 4
Start Page Number: 533
End Page Number: 549
Publication Date: Dec 2009
Journal: Journal of Global Optimization
Authors: , ,
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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