2010 Fiscal Year Final Research Report
Information Geometry of Convex Optimization : Extension and Applications
| Project/Area Number |
20340024
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | National Graduate Institute for Policy Studies (2010)
The Institute of Statistical Mathematics (2008-2009) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
OHARA Atsumi 福井大学, 工学研究科, 教授 (90221168)
MURAMATSU Masakazu 電気通信大学, 情報理工学研究科, 教授 (70266071)
FUKUDA Mituhiro 東京工業大学, 情報理工学研究科, 准教授 (80334548)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 凸最適化 / 情報幾何 / 内点法 / 数理計画 / 計算複雑度 / 制御理論 |
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| Research Abstract |
Interior-point algorithms for semidefinite programs and symmetric cone programs are analyzed in view of information geometry to show that the iteration complexity of primal-dual interior-point algorithms is approximately represented as a infomration geometric integral over central trajectory. Through extensive numerical experiments we demonstrated that the integral very accurately predict iteration-complexity of interior-point algorithms. One of the largest Gaussian graphical models in the world are successfully solved with super computer. Primal-dual interior-pont algorithms for large-scale Gaussian graphical models are developed. Regularization and facial reduction approaches for ill-conditioned semidefinite programs are developed.
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