Interval convex quadratic programming problems in a general form

Milan Hladík ()
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Milan Hladík: Charles University

Central European Journal of Operations Research, 2017, vol. 25, issue 3, No 12, 725-737

Abstract: 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.

Keywords: Convex quadratic programming; Interval analysis; Uncertainty modeling; 90C20; 90C31; 90C70 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10100-016-0445-8

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