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Interval convex quadratic programming problems in a general form

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  • Milan Hladík

    (Charles University)

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.

Suggested Citation

  • Milan Hladík, 2017. "Interval convex quadratic programming problems in a general form," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 725-737, September.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:3:d:10.1007_s10100-016-0445-8
    DOI: 10.1007/s10100-016-0445-8
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