Exact solution to a parametric linear programming problem
type: Item
instance of: scholarly article
title: Exact solution to a parametric linear programming problem
zbMATH Open document ID: 1395.90178
author: Iwona Skalna
author: Lubomir Kolev
published in: Numerical Algorithms
publication date: 2018-08-10T00:00:00Z
review text: The objective of the present paper is to exploit a new type of \(p\)-solution (\(x(p)=Lp+a\)) to address the following parametric linear programming (PLP) problem \(l(x, p)=c^T(p) x\), with \(c_i(p)\) nonlinear functions of \(p\). The PLP problem is a parametric generalization of the interval linear programming (ILP) problem, and more complex since \(x\) is an implicit function of \(p\). In this respect, the authors propose an iterative method for solving a system of linear interval parametric (LIP) equation, its computational scheme of the method and four versions of a simple polynomial complexity iterative method for determining the interval hull solution of the PLP problem. The results obtained for a numerical example show that this version of the method is efficient.
reviewed by: Doina Carp
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 65K15
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 6916368
zbMATH Keywords: \(p\)-solution
zbMATH Keywords: linear interval parametric system
zbMATH Keywords: parametric linear programming
zbMATH Keywords: interval hull solution
MaRDI profile type: Publication
full work available at URL: s11075-017-0418-6
OpenAlex ID: W2758502400
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DOI: 10.1007/S11075-017-0418-6
description: scientific article; zbMATH DE number 6916368