| Project/Area Number |
11440033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
KAWASAKI Hidefumi Graduate School of Mathematics, Kyushu University, Ass. Prof., 大学院・数理研究院, 助教授 (90161306)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOYAMA Kazunori Toyama Univ., Faculty of Economics, Ass. Prof., 経済学部, 助教授 (70240207)
SHIRAISHI Shunsuke Toyama Univ., Faculty of Economics, Ass. Prof., 経済学部, 助教授 (60226313)
IWAMOTO Seiichii Graduate School of Economics, Kyushu University, Prof., 大学院・経済学研究院, 教授 (90037284)
HYAKUTAKE Hiroto Graduate School of Mathematics, Kyushu University, Ass. Prof., 大学院・数理研究院, 助教授 (70181120)
FUJITA Toshiharu Kyushu Institute of Tech., Faculty of Engineering, Lect., 工学部, 講師 (60295003)
笛田 薫 九州大学, 大学院・数理学研究院, 助手 (50253399)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | conjugate point / Jacobi equation / Riccati equation / variational problem / nonlinear programming / dynamic programming / fazzy optimization / convex programming / ファジィ最適化 / 非線形計画問題 / 動的計画 / 不変埋没原理 / パラメトリック最適化 / ファジィ / カオス性 / 変分法 / 微分不可能計画 / 逆理論 |
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| Research Abstract |
1, We have achieved the main goal "conjugate point theory for nonlinear programming problems". Namely, we have defined the Jacobi equation, conjugate points, strict conjugate points, and the Riccati equation for the nonlinear programming problems. We have described the optimality in terms of (strict) conjugate points. Furthermore, we have clarified the relationship between the solution of the Riccati equation and the pivots of the Hesse matrix. This research takes the lead in this area.
2, We have shown that decision process problems on the stochastic system under the fuzzy environment can be solved by a new recurrent method based on the invariant embedding principle. By this research, Iwamoto was awarded the Best Paper Award of the 8th Bellman Continuum in 2001. Also, we have introduced a new class of evaluations and dynamic programming methods into the mathematical finance under uncertainty. Furthermore, we proposed a primitive strategy that includes historical data of states and decisions for the class.
3, We have proposed a method to convert the maximum eigen-value problem of a positive reciprocal matrix in AHP into a convex programming problem, and we have proved the existence of the optimal solution.
4, We have given a KKT condition for a multiobjective convex programming problem without Slater's condition. Furthermore, we have shown the continuity of the epsilon- efficient set and the efficient set.
5, We have proposed a method that estimates the embedding dimension and delay time from chaotic time series with dynamic noise. On the above researches, we gave 18 lectures in international symposiums and 42 talks in domestic conferences. Furthermore, 39 articles were published or are (in press).
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