Excess information in parametric linear optimization

We consider a parameteric linear optimization problem (called primal) and its corresponding dual problem, where the parameters are the cost vector and the right-hand-side vector, respectively. This article characterizes those constraints of the primal problem (variables of the dual problem, respecti...

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Bibliographic Details
Published inOptimization Vol. 55; no. 5-6; pp. 555 - 568
Main Authors Goberna, M. A., Jornet, V., Molina, M.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.10.2006
Taylor & Francis LLC
Subjects
Excess of information
Linear inequality systems
Linear programming
Linear semi-infinite programming
Mapping
Mathematics Subject Classifications 2000
Optimization
Parameter optimization
Redundancy
Studies
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Summary:We consider a parameteric linear optimization problem (called primal) and its corresponding dual problem, where the parameters are the cost vector and the right-hand-side vector, respectively. This article characterizes those constraints of the primal problem (variables of the dual problem, respectively) which can be eliminated without modifying its feasible set mapping its optimal set mapping, and its value mapping. Superfluity relative to the primal feasible set is nothing else than redundancy in its constraints system, whereas superfluity relative to the dual optimal set is closely related with another well-known phenomenon of excess of information in linear optimization: strong strangeness. The relationships between all these phenomena are also analyzed.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930600808350