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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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / 非線形スカラー化 / ミニマックス不等式 / 集合値写像 / 半順序空間 / 包絡分析法(DEA) / Ekelandの変分原理 |
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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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Report
(4 results)
Research Products
(87 results)
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[Presentation] Some minimax theorems for set-valued maps2011
Author(s)
Tamaki Tanaka
Organizer
The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議,NACA2011)
Place of Presentation
韓国・釜山・国立釜慶大学校(Pukyong National University, Pusan, Korea)(招待講演)
Year and Date
2011-08-04
Related Report
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[Presentation] Saddle point theorems for set-valued maps2011
Author(s)
Issei Kuwano
Organizer
The Seventh International Conference on Nonlinear Analysis and Convex Analysis(非線形解析学と凸解析学に関する第7回国際会議,NACA2011)
Place of Presentation
韓国・釜山・国立釜慶大学校(Pukyong National University, Pusan, Korea)
Year and Date
2011-08-04
Related Report
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