Development of Stable Methods and Solvers for Numerically Ill-conditioned Nonlinear Optimization Problems
| Project/Area Number |
15K21522
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Social systems engineering/Safety system
Mathematical informatics
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| Research Institution | Kansai University |
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Principal Investigator |
Dan Hiroshige 関西大学, 環境都市工学部, 准教授 (30434822)
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| Research Collaborator |
Matsumoto Yuya
Noguchi Masashi
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非線形最適化 / ソルバ / 多倍長精度計算 / 自動微分 |
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| Outline of Final Research Achievements |
In this research, our group has researched numerically ill-conditioned nonlinear optimization problems (NLPs). It is well known that there exist some NLPs which are difficult to find an optimal solution because numerical conditions are getting worse while we solve them.
To overcome such difficulties, our group has developed an NLP solver with multiple precision arithmetic which enables us to perform arbitrary precision arithmetic. Also, by using this solver, our group has shown the existence of NLPs which cannot be solved by double precision and can be solved by multiple precision.
Moreover, our group has observed the numerical behavior of the Maratos effect: it is a phenomenon which deteriorates the fast convergence in the neighborhood of the optimal solution. As a result, our group has shown that the region in which the Maratos effect occurs is limited.
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Report
(4 results)
Research Products
(11 results)
