Interval convex quadratic programming problems in a general form

Interval convex quadratic programming problems in a general form This paper addresses the problem of computing the minimal and the maximal optimal value of a convex quadratic programming (CQP) problem when the coefficients are subject to perturbations in given intervals. Contrary to the previous results concerning on some special forms of CQP only, we present a unified method to deal with interval CQP problems. The problem can be formulated by using equation, inequalities or both, and by using sign-restricted variables or sign-unrestricted variables or both. We propose simple formulas for calculating the minimal and maximal optimal values. Due to NP-hardness of the problem, the formulas are exponential with respect to some characteristics. On the other hand, there are large sub-classes of problems that are polynomially solvable. For the general intractable case we propose an approximation algorithm. We illustrate our approach by a geometric problem of determining the distance of uncertain polytopes. Eventually, we extend our results to quadratically constrained CQP, and state some open problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Central European Journal of Operations Research Springer Journals

Interval convex quadratic programming problems in a general form

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Business and Management; Operations Research/Decision Theory
ISSN
1435-246X
eISSN
1613-9178
D.O.I.
10.1007/s10100-016-0445-8
Publisher site
See Article on Publisher Site

Abstract

This paper addresses the problem of computing the minimal and the maximal optimal value of a convex quadratic programming (CQP) problem when the coefficients are subject to perturbations in given intervals. Contrary to the previous results concerning on some special forms of CQP only, we present a unified method to deal with interval CQP problems. The problem can be formulated by using equation, inequalities or both, and by using sign-restricted variables or sign-unrestricted variables or both. We propose simple formulas for calculating the minimal and maximal optimal values. Due to NP-hardness of the problem, the formulas are exponential with respect to some characteristics. On the other hand, there are large sub-classes of problems that are polynomially solvable. For the general intractable case we propose an approximation algorithm. We illustrate our approach by a geometric problem of determining the distance of uncertain polytopes. Eventually, we extend our results to quadratically constrained CQP, and state some open problems.

Journal

Central European Journal of Operations ResearchSpringer Journals

Published: Jun 21, 2016

References

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