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整数规划中的正则分解
引用本文:王涵,朱春钢.整数规划中的正则分解[J].数学研究及应用,2018,38(2):194-206.
作者姓名:王涵  朱春钢
作者单位:大连理工大学数学科学学院, 辽宁 大连 116024,大连理工大学数学科学学院, 辽宁 大连 116024
基金项目:国家自然科学基金项目(Grant Nos.11671068; 11271060), 民用飞机专项资助项目(Grant No.MJ-F-2012-04), 中央高校基本科研业务专项基金项目(Grant No.DUT16LK38).
摘    要:In this paper, we study the problem of regular decomposition in integer programming. We apply the radical of binomial ideal and universal Gr¨obner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set.

关 键 词:整数规划    正则分解    二项式理想    全局Gr\"{o}bner基    state  polytope
收稿时间:2017/6/7 0:00:00
修稿时间:2017/7/20 0:00:00

Regular Decomposition in Integer Programming
Han WANG and Chungang ZHU.Regular Decomposition in Integer Programming[J].Journal of Mathematical Research with Applications,2018,38(2):194-206.
Authors:Han WANG and Chungang ZHU
Institution:School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China and School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
Abstract:In this paper, we study the problem of regular decomposition in integer programming. We apply the radical of binomial ideal and universal Gr\"{o}bner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set.
Keywords:integer programming  regular decompositions  binomial ideal  universal Gr\"{o}bner bases  state polytope
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