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On parametric linear programming problems with fixed matrix of constraints 

Author: Horst Weinert a
Affiliation:   a Zentral.-Inst. f. Math. Mech, Berlin
DOI: 10.1080/02331887208801097
Publication Frequency: 6 issues per year
Published in: journal Statistics, Volume 3, Issue 6 1972 , pages 407 - 417
Formats available: PDF (English)
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Abstract

In order to define the notion “solution” of an arbitary parametric linear programming problem with constant matrix of constraints whose coefficients of the objective function as well as the components of the right hand side vector depend in a very general manner on the parameters there are introduced some usefull notions. The most important among them is the “structure of a solution” which yields a partion of the set P of all parameters under consideration firstly into the unsolvability set P0 and the solvability set PL which as complement to P0 is an open set with respect to P. The set PL can be divided into a finite number of maximal closed with respect to P subsets which are characterized by a certain structure. The desired notion “solution” for a general parametric linear programming problem then represents finitely many pairs containing a partition set together with the corresponding structure. Besides of this mainly investigations there are studied unicity of a partition and related questions.
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