Studies on discrete convex analysis and discrete fixed point theorems
| Project/Area Number |
23540142
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu University |
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Principal Investigator |
KAWASAKI Hidefumi 九州大学, 数理(科)学研究科(研究院), 教授 (90161306)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 最適化理論 / ゲーム理論 / 不動点定理 / ナッシュ均衡 / 組合せ最適化 / 離散凸解析 / 劣モジュラ解析 / 離散不動点定理 / Spernerの補題 / Brouwerの不動点定理 / Hexの定理 / 純戦略ナッシュ均衡 / n人非協力ゲーム |
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| Outline of Final Research Achievements |
We studied continuous and discrete structure in optimization theory and game theory with fixed point theorems and convex analysis at the core. We have verified theorems of discrete convex analysis and obtained some extensions. We gave a new proof of convex extension of L-convex functions and proved the inverse of the theorem. We have extended the separation theorem of L-convex sets to three or more L-convex sets. We have studied the relationship between Brouwer's thm., Spernar's lemma, Hex thm., and so on, and presented a sufficient condition that a mapping from the vertices of equilateral subdivision of the standard simplex into itself has a discrete fixed point on each completely labeled subsimplex. We have typed 260 pages of a book titled "Continuous and discrete structure of equilibria and extrema".
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Report
(5 results)
Research Products
(19 results)
