2000 Fiscal Year Final Research Report Summary
Smoothing Newton methods for nonsmooth equations
| Project/Area Number |
11640119
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Shimane University |
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Principal Investigator |
CHEN Xiaojun Shimane University, Faculty of Science and Engineering, Associate Professor, 総合理工学部, 助教授 (70304251)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUSHIMA Masao Kyoto University Graduate School of Informatics, Professor, 情報学研究科, 教授 (30089114)
YAMAMOTO Tetsuro Ehime University Faculty of Science, Professor, 理学部, 教授 (80034560)
YAMASAKI Maretsugu Shimane University, Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (70032935)
SUGIE Jitsuro Shimane University, Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (40196720)
FURUMOCHI Tetsuo Shimane University, Faculty of Science and Engineering, Professor, 総合理工学部, 教授 (40039128)
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| Project Period (FY) |
1999 – 2000
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| Keywords | nonsmooth equations / smoothing methods / Newton methods / convergence analysis |
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| Research Abstract |
In 1999-2000, the head investigator has published 15 papers with investigators Yamasaki, Yamamoto and Fukushima, and other international researchers on smoothing methods for nonsmooth equations. The main results are as follows.
i. Proposed a verification method for existence of solution of nonsmooth equations arising from complementarity problems.
ii. Introduced the slant differentiability for nonsmooth operators in Banach spaces. Using the slant differentiability, superlinear convergence of Newton-type methods for nonsmooth equations in Banach spaces is proved.
iii. Established some important properties of the trajectory defined by the Big-M smoothing method and global convergence of the method for P0 matrix linear complementarity problems.
iv. Presented a superlinearly and globally convergent method for reaction and diffusion problems with a non-Lipschitz operator.
v. Gave new error bounds for finite difference methods for Dirichlet problems with a nondifferentiable term.
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