2022 Fiscal Year Final Research Report
Research on Discrete Convex Analysis Approach for Robust Nonlinear Integer Programming Problems
| Project/Area Number |
18K11177
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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 | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | 離散凸関数 / ロバスト最適化 / 離散最適化 / 離散凸解析 / 整数計画 |
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| Outline of Final Research Achievements |
Discrete convex integer programming problem is a discrete optimization problem to find an integral vector minimizing a given discrete convex function under a given constraint. In this research, we consider a new problem called "a robust discrete convex integer programming problem" in which uncertainty arises in problem input. Based on my previous research results, we aimed at developing algorithms for this new problem which has theoretical guarantee in the quality of an obtained solution and computation time. We obtained various interesting results on robust version of several discrete optimization problems.
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| Free Research Field |
離散最適化
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| Academic Significance and Societal Importance of the Research Achievements |
既存の離散最適化アルゴリズムは問題の入力データが正確に与えられたと言う前提で適用されるが，実際に解くべき問題においては，与えられた入力データが正確に分からないという状況が一般的である．このような理論と現実のギャップを埋めるための一助として，本研究成果は役立つと考えている．また，現実問題からの要請に基づき新たな問題の枠組みを提案したが，これにより研究の新たな方向性を見いだすことができ，離散最適化分野のさらなる発展に貢献できるものと思われる．
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