| Project/Area Number |
26540007
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Iwata Satoru 東京大学, 大学院情報理工学系研究科, 教授 (00263161)
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| Co-Investigator(Kenkyū-buntansha) |
武田 朗子 統計数理研究所, 数理・推論研究系, 教授 (80361799)
中務 佑治 東京大学, 大学院情報理工学系研究科, 助教 (10723554)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 数理最適化 / 大域最適化 / 一般化固有値計算 / 機械学習 / 楕円体 / 信頼領域法 / 統計的機械学習 |
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| Outline of Final Research Achievements |
Nonconvex optimization is believed to refuse any efficient algorithms in general. This project has aimed at developing a method to design efficient algorithms for nonconvex optimization problems that arises with a geometric background, exploiting their structures. In particular, we have designed an algorithm for computing the signed distance between overlapping ellipsoids. The running time is O(n^6), where n is the dimension of the space. We have extended this approach to solve the generalized CDT problem in the same running time. We have also reduced the trust-region subproblem, which is repeatedly solved in the trust-region method, to a generalized eigenvalue problem, and shown that this reduction leads to an efficient and accurate solution method with the aid of today's highly developed solvers for the generalized eigenvalue problem.
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