2023 Fiscal Year Final Research Report
Research on resource allocation problems by discrete convex analysis
| Project/Area Number |
20K11697
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | The Institute of Statistical Mathematics (2021-2023)
Tokyo Metropolitan University (2020) |
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Principal Investigator |
Murota Kazuo 統計数理研究所, 大学統計教員育成センター, 特任教授 (50134466)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 離散凸解析 / 最適化理論 / 数理工学 / 情報基礎 / アルゴリズム / 経済理論 |
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| Outline of Final Research Achievements |
Discrete Convex Analysis is a theory of optimization that connects continuous optimization and discrete optimization by establishing a general framework for discrete optimization comparable to the conventional convex analysis in the continuous setting. In this research project we aimed at developing a general framework for discrete resource allocation problems on the basis of the duality theory in discrete convex analysis. We have obtained theoretical results and algorithms for discrete structures such as M-convex sets (sets of integer points in an integral base polyhedron), M2-convex sets (sets of integer points in the intersection two integral base polyhedra), integral network flows, and integral submodular flows.
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| Free Research Field |
数理工学
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| Academic Significance and Societal Importance of the Research Achievements |
離散凸解析は，最適化において「連続と離散を繋ぐパラダイム」であり，様々な分野で別々に考察されてきた数学的な構造を，分野を越えて理解して，相互に利用するための枠組みである．離散凸解析の理論やアルゴリズムが一般的な形で整理されることによって，コンピュータ科学，オペレーションズ・リサーチ，経済学，ゲーム理論，数学などの様々な分野での共通の言葉やアプローチが生まれ，学問諸分野の交流が可能となる．さらには，その共通の知識に基づいて，様々な応用が繋がり発展していくことが期待される．
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