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

Guoyin Li ()
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Guoyin Li: University of New South Wales

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 3, No 9, 710-726

Abstract: 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.

Keywords: Quadratic optimization; Bivalent constraints; Global optimality conditions (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9930-3

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