Development of practical derivative-free algorithms for optimization
| Project/Area Number |
25330022
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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 |
Mathematical informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
Kuno Takahito 筑波大学, システム情報系, 教授 (00205113)
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| Co-Investigator(Kenkyū-buntansha) |
AKIKO YOSHISE 筑波大学, システム情報系, 教授 (50234472)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 数理計画法 / 非線形最適化 / 大域的最適化 / 最適化アルゴリズム / 分枝限定法 / 数理最適化 / 確定的アルゴリズム |
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| Outline of Final Research Achievements |
The major results of this research are two deterministic algorithms for solving concave minimization problems to global optimality. The one belongs to the class of branch-and-bound algorithms, referred to as the conical algorithm, which subdivides the feasible set using a number of cones and computes a lower bound of the objective function on each. We developed a new rule for cone subdivision, named w-bisection, and proved the convergence of the algorithm according to it. Our numerical experiments indicated that our new subdivision rule is rather promising. The other is a kind of simplicial algorithm which subdivides the feasible set using simplices and carries out lower-bounding on each. We generalized existing w-subdivision, w-bisection, and proposed w-k-section. Under this simplex subdivision rule, we proved the convergence of the algorithm, and implemented numerical experiments, which demonstrated an advantage of w-k-section compared with other existing subdivision rules.
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Report
(4 results)
Research Products
(8 results)
