Steepest-edge rule and its number of simplex iterations for a nondegenerate LP

Masaya Tano; Ryuhei Miyashiro; Tomonari Kitahara

doi:10.1016/j.orl.2019.02.003

Steepest-edge rule and its number of simplex iterations for a nondegenerate LP

Masaya Tano, Ryuhei Miyashiro, Tomonari Kitahara

mathematics and information

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Abstract

In this paper, we consider the number of simplex iterations with the steepest-edge rule for the simplex method. For a nondegenerate linear programming problem, we show two upper bounds for the number of iterations of the simplex method with the steepest-edge rule via analysis of the p-norm rule, which is a previously proposed generalization of the steepest-edge rule.

Original language	English
Pages (from-to)	151-156
Number of pages	6
Journal	Operations Research Letters
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/j.orl.2019.02.003
Publication status	Published - May 2019

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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title = "Steepest-edge rule and its number of simplex iterations for a nondegenerate LP",

abstract = "In this paper, we consider the number of simplex iterations with the steepest-edge rule for the simplex method. For a nondegenerate linear programming problem, we show two upper bounds for the number of iterations of the simplex method with the steepest-edge rule via analysis of the p-norm rule, which is a previously proposed generalization of the steepest-edge rule.",

author = "Masaya Tano and Ryuhei Miyashiro and Tomonari Kitahara",

note = "Funding Information: This work was partially supported by JSPS KAKENHI, Japan Grant Numbers JP17K01246 and JP15K15941 .",

year = "2019",

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T1 - Steepest-edge rule and its number of simplex iterations for a nondegenerate LP

AU - Tano, Masaya

AU - Miyashiro, Ryuhei

AU - Kitahara, Tomonari

N1 - Funding Information: This work was partially supported by JSPS KAKENHI, Japan Grant Numbers JP17K01246 and JP15K15941 .

PY - 2019/5

Y1 - 2019/5

N2 - In this paper, we consider the number of simplex iterations with the steepest-edge rule for the simplex method. For a nondegenerate linear programming problem, we show two upper bounds for the number of iterations of the simplex method with the steepest-edge rule via analysis of the p-norm rule, which is a previously proposed generalization of the steepest-edge rule.

AB - In this paper, we consider the number of simplex iterations with the steepest-edge rule for the simplex method. For a nondegenerate linear programming problem, we show two upper bounds for the number of iterations of the simplex method with the steepest-edge rule via analysis of the p-norm rule, which is a previously proposed generalization of the steepest-edge rule.

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DO - 10.1016/j.orl.2019.02.003

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JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 3

ER -

Steepest-edge rule and its number of simplex iterations for a nondegenerate LP

Abstract

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