Structural Analysis of Mathematical Programming based on CombinatorialMatrix Theory
| Project/Area Number |
21760057
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 組合せ最適化 / 定性的行列理論 / 疎性 / マッチング / グラフアルゴリズム / 点素サイクル / ナップサック問題 / フィードバック点集合 / 線形相補性問題 / ビンパッキング問題 / 近似アルゴリズム / 組合せ的行列理論 / 数理計画 / 半正定値対称行列 |
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| Research Abstract |
Mathematical programming is a branch of mathematics concerned with optimization problems, in which one aims to find the best solution subject to some constraints, and it can be applied to a variety of engineering fields such as operations research. Combinatorial matrix theory is an approach to understand matrix structure using combinatorial methodology, which is useful for structural analysis of large linear systems in practice. In this research, we have analyzed mathematical programming problems based on combinatorial properties such as sign patterns or sparsity. In addition, we have developed combinatorial matrix theory in terms of mathematical programming applications.
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Report
(4 results)
Research Products
(34 results)
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[Presentation] Robust Independence Systems2011
Author(s)
N. Kakimura and K. Makino
Organizer
The 38th International Colloquium on Automata
Place of Presentation
Languages and Programming (ICALP 2011), Zurich, Switzerland
Related Report
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