Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method

Akiko Takeda, Masakazu Kojima, Katsuki Fujisawa

研究成果: Contribution to journalArticle査読

14 被引用数 (Scopus)

抄録

An interesting combinatorial (enumeration) problem arises in the initial phase of the polyhedral homotopy continuation method for computing all solutions of a polynomial equation system in complex variables. It is formulated as a problem of finding all solutions of a specially structured system of linear inequalities with a certain additional combinatorial condition. This paper presents a computational method for the problem fully utilizing the duality theory and the simplex method for linear programs, and report numerical results on a single cpu implementation and a parallel cpu implementation of the method.

本文言語英語
ページ(範囲)64-82
ページ数19
ジャーナルJournal of the Operations Research Society of Japan
45
1
DOI
出版ステータス出版済み - 2002
外部発表はい

All Science Journal Classification (ASJC) codes

  • 決定科学(全般)
  • 経営科学およびオペレーションズ リサーチ

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