| Project/Area Number |
26400207
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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 | Akita Prefectural University |
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Principal Investigator |
Yutaka Kimura 秋田県立大学, システム科学技術学部, 教授 (10315616)
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| Co-Investigator(Kenkyū-buntansha) |
岩本 誠一 九州大学, 経済学研究院, 名誉教授 (90037284)
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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 |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 双対化 / 意思決定 / 最適化 / 2次計画 / 意思決定最適化問題 / 不等式双対化 |
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| Outline of Final Research Achievements |
In this research, we propose some dualization methods and investigate a mutual relationship between optimal points and optimal values for a class of quadratic programming problems, which include problems with decision making and optimization. We have discussed over and over again how to derive dual problems from primal problems and vice versa. And we have succeeded in deriving three dualization methods which are called dynamic dualization, plus-minus dualization, and inequality dualization. Moreover, it is shown that the optimal solutions for quadratic programming problem are characterized by the Fibonacci numbers or the Golden number. We have established some duality theorems for quadratic programming problem, which are called Fibonacci complementary duality, Golden complementary duality, and so on.
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