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Exact solution to a parametric linear programming problem

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Abstract

We consider the problem of determining the interval hull solution l ∗ to a parametric linear programming (PLP) problem l(x, p) = c T(p)x, where c i (p) can be in general nonlinear functions of p, and x satisfy the constraint A(p)x = b(p), p ∈ p. A new iterative method for determining l ∗ is suggested. The method exploits the concept of the p-solution to a square linear interval parametric (LIP) system, having the parametric form x(p) = L p + a, p ∈ p, where L is a real n × m matrix (n and m are, respectively, the sizes of the square matrix A and vector p), whereas a is an interval vector. A numerical example is provided to illustrate the new approach.

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Authors and Affiliations

  1. Technical University of Sofia, 1000, Sofia, Bulgaria

    Lubomir Kolev

  2. AGH University of Science and Technology, Aleja Adama Mickiewicza 30, 30-059, Kraków, Poland

    Iwona Skalna

Authors
  1. Lubomir Kolev
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  2. Iwona Skalna
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Correspondence to Lubomir Kolev.

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Kolev, L., Skalna, I. Exact solution to a parametric linear programming problem. Numer Algor 78, 1183–1194 (2018). https://doi.org/10.1007/s11075-017-0418-6

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  • DOI: https://doi.org/10.1007/s11075-017-0418-6

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