Convex Optimization Modeling and Computational Inference
| Project/Area Number |
24310112
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | National Graduate Institute for Policy Studies |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OHARA Atsumi 福井大学, 工学(系)研究科, 教授 (90221168)
MURAMATSU Masakazu 電気通信大学, 情報理工学(系)研究科, 教授 (70266071)
FUKUDA Mitsuhiro 東京工業大学, 情報理工学(系)研究科, 准教授 (80334548)
UENO Genta 統計数理研究所, 大学共同利用機関等の部局等, 准教授 (40370093)
KITAHARA Tomonari 東京工業大学, 社会理工学研究科, 助教 (10551260)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
Fiscal Year 2014: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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| Keywords | 凸最適化 / 半正定値計画 / 2次錐計画 / 双対性 / 制御理論 / データ同化 / メソポタミア / 半正定値計画問題 / 面縮小法 / 内点法 / 弱実行不能 / 悪条件 / ２次錐計画 / 古代メソポタミア / 社会構造推定 / von Neumann エントロピー / 大規模最適化 / 人口動態推定 / 大規模問題 / 悪条件性 / モデリング |
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| Outline of Final Research Achievements |
We studied modeling, mathematics and algorithms of convex optimization. Semidefinite programs and second-order cone programs are convex optimization problems studied intensively recently because of their broad applicability but yet hard to solve. To overcome this difficulty, we analyzed structures of problems with nonzero duality gap and/or unattained optimality, and of weakly infeasible problems. We also developed a self-concordant barrier function for optimization problem involving von Neumann entropy function. Regarding modeling, we studied clay tablet data from Nuzi, an ancient village in Mesopotamia existed 3500 years ago. We formulated estimation problem of birth and death years of individuals appearing in the tablets and generated years of tablets as a convex quadratic program. The result suggested that wealth is generally concentrated to a few rich family over about a hundred year of period. Finally, we also studied optimization methods for ocean data assimilation.
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Report
(5 results)
Research Products
(25 results)
