Study on Set-Valued Inequalities based on Set-Valued Analysis and Convex Analysis and its Applications to Optimization Problems
| Project/Area Number |
26400194
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied 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) |
木村 泰紀 東邦大学, 理学部, 教授 (20313447)
黒岩 大史 島根大学, 総合理工学研究科, 教授 (40284020)
山田 修司 新潟大学, 自然科学系, 教授 (80331544)
劉 雪峰 新潟大学, 自然科学系, 准教授 (50571220)
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| Co-Investigator(Renkei-kenkyūsha) |
TANINO Tetsuzo 大阪大学, 名誉教授 (50125605)
MATSUSHITA Shinya 秋田県立大学, システム科学技術学部, 准教授 (20435449)
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| Research Collaborator |
SUZUKI Satoshi 島根大学, 総合理工学研究院, 助教 (70580489)
KIMURA Kenji 芝浦工業大学, 工学部, 非常勤講師
HIGUCHI Masakazu 埼玉大学, 大学院理工学研究科, 産学官連携研究員
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 集合最適化 / ベクトル最適化 / 劣線形スカラー化 / 集合値写像 / スカラー化関数 / 二者択一の定理 / ファジィ集合 / 数値計算法 / 集合値計画 / 非線形スカラー化 / ミニマックス不等式 / 集合値最適化 / 凸解析学 / 半順序空間 |
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| Outline of Final Research Achievements |
In this study, we give several applications by using nonlinear scalarization methods for sets and proposed computational scheme for the scalarizing fucntions. This approach has been proposed in the previous study (research 21540121 supported by Grant-in-Aid for Scientific Research (C)). First, we clarified the inherited properties of the composite function of a monotonic scalarizing function and a sort of convex set-valued map systematically. As the results, we had several applications on certain generalization of Ricceri's nonlinear inequality to set-valued maps, alternative theorem for set-valued maps, and also we developed computational methods to evaluate the scalarizing functions and some construction of difference evaluation functions for fuzzy sets. Besides, we studied multicriteria two-persons zero-sum matrix games, algebraic properties of weak efficient solutions for sets, and hierarchical equilibrium problems including fixed-point problems.
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Report
(4 results)
Research Products
(40 results)
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[Presentation] Alternative theorems via set-valued analysis2016
Author(s)
Gue Myung Lee, Jae Hyoung Lee, Yuto Ogata, Yutaka Saito, Tamaki Tanaka
Organizer
The 5th Asian Conference on Nonlinear Analysis and Optimization (NAO-Asia2016)
Place of Presentation
朱鷺メッセ，新潟（日本）
Year and Date
2016-08-01
Related Report
Int'l Joint Research
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[Presentation] Generalized alternative theorems based on set-relations2016
Author(s)
Yuto Ogata, Yutaka Saito, Tamaki Tanaka, Gue Myung Lee, Jae Hyoung Lee
Organizer
The 9th Asian Conference on Fixed point theory and Optimization (ACFPTO2016)
Place of Presentation
King Mongkut's University of Technology Thonburi (KMUTT), バンコク（タイ）
Year and Date
2016-05-18
Related Report
Int'l Joint Research / Invited
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