2011 Fiscal Year Final Research Report
Study on Nonlinear Scalarization Methods for Set-Valued Maps and its Applications into Mathematical Programming
| Project/Area Number |
21540121
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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 | Niigata University |
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Principal Investigator |
TANAKA Tamaki 新潟大学, 自然科学系, 教授 (10207110)
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| Co-Investigator(Kenkyū-buntansha) |
ISOGAI Eiichi 新潟大学, 自然科学系, 教授 (40108014)
YAMADA Syuuji 新潟大学, 自然科学系, 准教授 (80331544)
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| Co-Investigator(Renkei-kenkyūsha) |
TANINO Tetsuzo 大阪大学, 大学院・工学研究科, 教授 (50125605)
KUROIWA Daishi 島根大学, 総合理工学部, 教授 (40284020)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 集合値計画 / 非線形スカラー化関数 / 均衡問題 / 集合値最適化 / ベクトル最適化 / 凸解析学 / 数理計画問題 / 大域的最適化 |
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| Research Abstract |
In this study, we give theoretical analysis on nonlinear scalarization methods for sets, which has been introduced in the previous study(research 21540121 supported by Grant-in-Aid for Scientific Research(C)), and we research algorithm development for its numerical calculations and its applications. That is to say we derive several mathematical properties related to certain inequalities for set-valued maps by the help of classical theory through the use of the invariant property of some scalarization methods for set-relationship.
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