AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

TOMONARI KITAHARA; SHINJI MIZUNO

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AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

机译：带有任何输入规则选择的原始单纯形法生成的不同解的数量的上界

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摘要

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

机译：最近，北原和美津浓通过Dantzig（最负的）枢轴定律推导了由原始单纯形法生成的不同解的数量上限。在本文中，我们获得了任何数据透视规则的上限，该规则选择了一个输入变量，该变量的每次迭代所降低的成本为负。上限适用于具有完全单模矩阵的线性规划问题。我们还获得了对偶单纯形法的相似上限。

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来源
《Asia-Pacific Journal of Operational Research》 |2013年第3期|1340012.1-1340012.10|共10页
作者
TOMONARI KITAHARA; SHINJI MIZUNO;
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作者单位

Department of Industrial Engineering and Management Tokyo Institute of Technology, 2-12-1-W9-62 Oo-Okayama, Meguro, Tokyo, 152-8552, Japan;

Department of Industrial Engineering and Management Tokyo Institute of Technology, 2-12-1-W9-58 Oo-Okayama, Meguro, Tokyo, 152-8552, Japan;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Linear programming; the number of basic solutions; pivoting rule; the simplex method;

机译：线性规划;基本解决方案的数量;枢轴规则单纯形法;

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1. Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied [J] . Adrienn Csizmadia, Zsolt Csizmadia, Tibor Illés Central European journal of operations research: CEJOR . 2018,第3期

机译：应用S-MONOTONE索引选择规则时二次原始单纯x方法的有限度
2. A bound for the number of different basic solutions generated by the simplex method [J] . Tomonari Kitahara, Shinji Mizuno Mathematical Programming . 2013,第1a2期

机译：单纯形法生成的不同基本解的数量的界限
3. Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal [J] . Joshi Mark S. Quantitative finance . 2016,第4期

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4. A Bound for the Number of Different Basic Solutions Generated by the Simplex Method [C] . Shinji Mizuno, Tomonari Kitahara The 8th international conference on optimization: Techniques and Applications . 2010

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5. Classification and variable selection for high dimensional multivariate binary data: Adaboost based new methods and a theory for the plug-in rule. [D] . Park, Junyong. 2006

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6. Examining variable selection methods for the predictive performance of regression models and the proportion of selected variables and selected random variables [O] . Hiromasa Kaneko 2021

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7. A Bound for the Number of Different Basic Solutions Generated by the Simplex Method [O] . Kitahara, Tomonari, Mizuno, Shinji 2011

机译：关于生成的不同基本解的数量的界限单纯形法

AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

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