Developments of inverse function theorems by variational analysis and applications to optimization problems
| Project/Area Number |
19740059
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Marine Science and Technology (2008-2009)
Kwansei Gakuin University (2007) |
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Principal Investigator |
SEKIGUCHI Yoshiyuki Tokyo University of Marine Science and Technology, 海洋工学部, 助教 (50434890)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,050,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥450,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | 非線形関数解析 / 変分解析 / 最適化理論 / 関数解析学 / 解析学 / 数理工学 / アルゴリズム / Variational Analysis / 逆関数定理 / Metric regularity / Lyusternikの定理 |
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| Research Abstract |
We considered metric regularity in variational analysis, focusing on its quantitative analysis through funciontal analytic methods and applications to inequality systems, which especially appear in optimization problems. Our main contributions are the following: 1. Exact estimates of modulus of metric regularity for inequality systems in Banach spaces are given. The key idea is to consider a sequence of equivalent norms on the space. 2. By generalizing the result of 1, regularity estimates for convex set-valued mappings between Banach spaces are given. 3. Formulas for normal cones to a set defined by continuous operators in Euclidean spaces are obtained. The arguments use calculus of subdifferentials repeatedly.
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Report
(4 results)
Research Products
(26 results)
