On parametric linear programming problems with fixed matrix of constraints
作者:
Horst Weinert,
期刊:
Mathematische Operationsforschung und Statistik
(Taylor Available online 1972)
卷期:
Volume 3,
issue 6
页码: 407-417
ISSN:0047-6277
年代: 1972
DOI:10.1080/02331887208801097
出版商: Akademie-Verlag
数据来源: Taylor
摘要:
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 setPof all parameters under consideration firstly into the unsolvability setP0and the solvability setPLwhich as complement toP0is an open set with respect toP. The setPLcan be divided into a finite number of maximal closed with respect toPsubsets 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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