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Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition

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Abstract

In this paper, we establish global optimality conditions for quadratic optimization problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimization problems with quadratic equality and bivalent constraints. Then we examine situations where this optimality condition is equivalent to checking the positive semidefiniteness of a related matrix, and so, can be verified in polynomial time by using elementary eigenvalues decomposition techniques. As a consequence, we also present simple sufficient global optimality conditions, which can be verified by solving a linear matrix inequality problem, extending several known sufficient optimality conditions in the existing literature.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia

    Guoyin Li

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  1. Guoyin Li
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Correspondence to Guoyin Li.

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Communicated by X.Q. Yang.

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Li, G. Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition. J Optim Theory Appl 152, 710–726 (2012). https://doi.org/10.1007/s10957-011-9930-3

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  • DOI: https://doi.org/10.1007/s10957-011-9930-3

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