Constructing the set of efficient objective values in multiple objective linear programs
type: Item
instance of: scholarly article
title: Constructing the set of efficient objective values in multiple objective linear programs
zbMATH Open document ID: 0706.90071
DOI: 10.1016/0377-2217(90)90011-Y
published in: European Journal of Operational Research
publication date: 1990-01-01T00:00:00Z
review text: The work is devoted to obtain proper descriptions for the set of all feasible objective values in finite vectorial multiple objective linear programs \[ (MOLP) \text{ ``maximize'' \(Cx\) subject to } x\in X \] where \(X=\{x\in R^ n:\) Ax\(\leq b\}\) and C is a linear mapping from \(R^ n\) to \(R^ k\) identified with a \(k\times n\) matrix (Proposition 3.1, Proposition 3.2) and to the elaboration of numerical algorithms for computing the range of C (Section 2), its efficient structure and the image of the polyhedron X by C (Section 3). The authors construct also a polyhedron which has the same efficient points as the set of objective values and all of its extreme points are Pareto-efficient. We note that it is not possible to transfer the results to infinite dimensional spaces.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 4160489
zbMATH Keywords: finite vectorial multiple objective linear programs
zbMATH Keywords: efficient points
zbMATH Keywords: Pareto-efficient
author: J. P. Dauer
author: O. A. Saleh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4160489