2009 Fiscal Year Final Research Report
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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| Keywords | 非線形関数解析 / 変分解析 / 最適化理論 |
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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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Research Products
(13 results)
