Global minimization of difference of quadratic and convex functions over box or binary constraints |
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Authors: | V Jeyakumar N Q Huy |
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Institution: | (1) Department of Applied Mathematics, University of New South Wales, Sydney, 2052, Australia;(2) Department of Mathematics, Hanoi Pedagogical University No. 2, Vinh Phuc, Vietnam |
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Abstract: | In this paper, we present necessary as well as sufficient conditions for a given feasible point to be a global minimizer of
the difference of quadratic and convex functions subject to bounds on the variables. We show that the necessary conditions
become necessary and sufficient for global minimizers in the case of a weighted sum of squares minimization problems. We obtain
sufficient conditions for global optimality by first constructing quadratic underestimators and then by characterizing global
minimizers of the underestimators. We also derive global optimality conditions for the minimization of the difference of quadratic
and convex functions over binary constraints. We discuss several numerical examples to illustrate the significance of the
optimality conditions.
The authors are grateful to the referees for their helpful comments and valuable suggestions which have contributed to the
final preparation of the paper. |
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Keywords: | Quadratic non-convex minimization Concave minimization Necessary optimality conditions Sufficient conditions Box constraints 0/1 Constraints |
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