| 整数规划中的正则分解 |
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| 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 |
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| 作者姓名： | 王涵 朱春钢 |
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| 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 |
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| 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). |
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| 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.
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| 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： | 2017-06-07 |
| 修稿时间： | 2017-07-20 |
Regular Decomposition in Integer Programming |
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| Han WANG and Chungang ZHU. Regular Decomposition in Integer Programming[J]. Journal of Mathematical Research with Applications, 2018, 38(2): 194-206 |
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| Authors: | Han WANG and Chungang ZHU |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | integer programming regular decompositions binomial ideal universal Gr" {o}bner bases state polytope |
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