| Project/Area Number |
15K04994
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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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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Niigata University |
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Principal Investigator |
YAMADA SYUUJI 新潟大学, 自然科学系, 教授 (80331544)
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| Co-Investigator(Kenkyū-buntansha) |
田中 環 新潟大学, 自然科学系, 教授 (10207110)
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| Research Collaborator |
TANINO tetsuzo
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 大域的最適化 / KKT条件 / 逆凸計画問題 / 2次計画問題 / 逆凸制約 / 分枝限定法 / 逆凸計画 / FJ条件 |
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| Outline of Final Research Achievements |
In this study, we propose a global optimization method for a reverse convex quadratic programming problem (QRC) whose feasible set is expressed as the area excluded the interior of a convex set from another convex set. It is known that many global optimization problems can be transformed into such a problem. Iterative solution methods for solving (QRC) have been proposed by many researchers. In order to find an approximate solution of a globally optimal solution of (QRC), we introduce a procedure for listing KKT points of (QRC). By utilizing such a procedure, we can calculate all KKT points contained in the intersection of the boundaries of convex sets defining the feasible set. Further, we propose an algorithm for finding a globally optimal solution of (QRC) by incorporating such a procedure into a branch and bound procedure.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は，逆凸2次計画問題に対し, KKT点列挙法を独自に開発し，従来法では近似解を求めることができなかった高次な問題に対しても精度の高い近似解を求めることができるアルゴリズムの開発に成功した。したがって，本研究は大域的最適化の視点から非常に独創的であり，学術的に高い意味を持つものと考える。また，多くの数理計画問題が本研究対象問題に変換できるため，本研究の成果は数理計画法の分野で幅広く活用されるものと予想できる。さらに，本研究成果は, 経営工学，ポートフォリオ選択問題，システム制御，都市計画，施設配置，輸送問題等に活用できるため, 幅広い分野に貢献できるものと期待できる。
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