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An interior point approach to postoptimal . . . (1993)
| Venue: | JOURNAL OF OPERATIONS RESEARCH |
| Citations: | 22 - 7 self |
BibTeX
@ARTICLE{Jansen93aninterior,
author = {B. Jansen and C. Roos and T. Terlaky},
title = {An interior point approach to postoptimal . . . },
journal = {JOURNAL OF OPERATIONS RESEARCH},
year = {1993}
}
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Abstract
In practice, understanding the behavior of the solution of the linear programming problem due to changes in the data is often as important as obtaining the optimal solution itself. Postoptimal analysis based on the simplex method by using an optimal basis is well established and widely used. However, in case of degenerate optimal solutions, due to nonunicity of optimal bases, problems arise in correct interpretation of the results of the analysis; partial, in a certain sense erroneous, information is e.g. provided by commercial packages for linear programming. We discuss the problems in this approach and the proposals that have been made to resolve the difficulties. Then we investigate postoptimal analysis in linear programming from an interior point of view. We make use of the partition of the variables induced by a pair of strictly complementary solutions (the optimal partition), which is uniquely determined and arises as a natural concept in interior point methods. We give example...
Keyphrases
interior point approach linear programming postoptimal analysis degenerate optimal solution natural concept optimal solution optimal basis simplex method optimal partition complementary solution commercial package correct interpretation certain sense interior point optimal base interior point method linear programming problem
