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On Solving an Optimization Problem with Interval Coefficients

In: Optimization Methods and Applications

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  • Andrii Bryla

    (Uzhhorod National University)

Abstract

In this paper, a decision-making problem where alternatives are estimated with interval parameters and the feasible set is defined using interval constraints is considered. Based on the assumption that the objective function and constraints are linear, a linear optimization problem with interval coefficients in the objective function and constraints was specified. For solving this problem, the approach of its reduction to optimization problem with a scalar objective function and scalar constraints was proposed. This approach consists of two steps. At the first step, we reduce the problem with interval coefficients to a lexicographical optimization problem with lexicographical constraints. At the second step, we reduce this lexicographic optimization problem to a problem with a single scalar objective function and scalar constraints. This makes it possible to use well-known classical methods of real-valued optimization theory for solving this problem.

Suggested Citation

  • Andrii Bryla, 2017. "On Solving an Optimization Problem with Interval Coefficients," Springer Optimization and Its Applications, in: Sergiy Butenko & Panos M. Pardalos & Volodymyr Shylo (ed.), Optimization Methods and Applications, pages 57-74, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-68640-0_4
    DOI: 10.1007/978-3-319-68640-0_4
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