Global minimization of difference of quadratic and convex functions over box or binary constraints

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...

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Bibliographic Details
Published inOptimization letters Vol. 2; no. 2; pp. 223 - 238
Main Authors Jeyakumar, V., Huy, N. Q.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2008
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Sufficient conditions
Quadratic non-convex minimization
0/1 Constraints
Necessary optimality conditions
Box constraints
Concave minimization
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Summary: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.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-007-0053-6