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.
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The author was supported by the Czech Science Foundation Grant P402/13-10660S.
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Hladík, M. Interval convex quadratic programming problems in a general form. Cent Eur J Oper Res 25, 725–737 (2017). https://doi.org/10.1007/s10100-016-0445-8
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DOI: https://doi.org/10.1007/s10100-016-0445-8