Optimal values range of interval polynomial programming problems

Amirmahmoodi, Somayeh; Mishmast Nehi, Hassan; Allahdadi, Mehdi

doi:10.22075/ijnaa.2021.23797.2611

Optimal values range of interval polynomial programming problems

Document Type : Research Paper

Authors

Somayeh Amirmahmoodi

Hassan Mishmast Nehi

Mehdi Allahdadi

Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran

10.22075/ijnaa.2021.23797.2611

Abstract

Uncertainty exists in many real-life engineering and mechanical problems. Here, we assume that uncertainties are caused by intervals of real numbers. In this paper, we consider the interval nonlinear programming (INLP) problems where the objective function and constraints include interval coefficients. So that the variables are deterministic and sign-restricted. Additionally, the constraints are considered in the form of inequalities. A basic task in INLP is calculating the optimal values range of objective function, which may be computationally very expensive. However, if the boundary functions are available, the problems become much easier to solve. By making these assumptions, an efficient method is proposed to compute the optimal values range using two classic nonlinear problems. Then, the optimal values range are obtained by direct inspection for a special kind of interval polynomial programming (IPP) problems. Two numerical examples are given to verify the effectiveness of the proposed method.

Keywords

Interval uncertainty

Interval nonlinear programming

Optimal values range

Interval polynomial

Boundary functions

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