On the number of solutions generated by the simplex method for LP

Tomonari Kitahara, Shinji Mizuno

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

抄録

We obtain upper bounds for the number of distinct solutions generated by the simplex method for linear programming (LP). One of the upper bounds is polynomial in the number of variables, the number of constraints, and the ratio of the maximum to the minimum positive components in all the basic feasible solutions. We show that they are good upper bounds for some special LP problems including those on 0-1 polytopes, those with totally unimodular matrices, and the Markov decision problems. We also show that the upper bounds are almost tight by using an LP instance on a 0-1 polytope and a simple variant of the Klee-Minty example.

本文言語英語
ホスト出版物のタイトルOptimization and Control Techniques and Applications
編集者Yi Zhang, Honglei Xu, Kok Lay Teo, Honglei Xu
出版社Springer New York LLC
ページ75-90
ページ数16
86
ISBN(電子版)9783662434031
DOI
出版ステータス出版済み - 1 1 2014
外部発表はい

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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