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...

Full description

Saved in:
Bibliographic Details
Published in:Optimization letters Vol. 2; no. 2; pp. 223 - 238
Main Authors: Jeyakumar, V., Huy, N. Q.
Format: Journal Article
Language:English
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
ISSN:1862-4472, 1862-4480
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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