2023 Fiscal Year Final Research Report
Development of approximation algorithms for M-convex function minimization
| Project/Area Number |
21K21290
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
1001:Information science, computer engineering, and related fields
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| Research Institution | Seikei University (2023)
Tokyo Metropolitan University (2021-2022) |
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Principal Investigator |
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| Project Period (FY) |
2021-08-30 – 2024-03-31
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| Keywords | 離散凸関数 / 離散凸解析 / 離散最適化 / アルゴリズム / Ｍ凸関数 / ジャンプシステム |
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| Outline of Final Research Achievements |
The concept of M-convex functions is a theoretical framework to solve discrete optimization problems in a unified manner. The minimization problem of M-convex functions can be regarded as a generalization of discrete optimization problems, such as the minimum spanning tree problem and the separate convex resource allocation problem. The optimal solution of M-convex function minimization can be obtained by using information on the steepest descent direction in which the function value decreases most within an appropriately defined neighborhood. In this study, we aimed to construct an algorithm that guarantees the solution's accuracy in situations where the steepest descent direction is not always available. As a result, we obtained an interesting result: the steepest descent algorithm has geodesic property for the problem of separable convex function minimization on jump systems, which is related to M-convex function minimization.
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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 |
M凸関数最小化問題に対するアルゴリズムの多くは，近傍内で最も関数値が減少する最急降下方向の情報を利用するが，現実の問題では最急降下方向を求めることが困難な状況が起こりうる．最終的に得られた結果は想定と異なるものになったが，ジャンプシステム上の分離凸関数最小化という多くの実行可能領域を表現可能な問題クラスについて理論的な成果が得られ，解きやすい離散最適化問題の離散構造の理解に貢献できたと考えられる．
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