| 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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| 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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