Development of successive iteration methods utilizing partial separating hyperplanes for a global optimization problem with a reverse convex constraint
| Project/Area Number |
24540118
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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 | Niigata University |
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Principal Investigator |
YAMADA Syuuji 新潟大学, 自然科学系, 教授 (80331544)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Tamaki 新潟大学, 自然科学系, 教授 (10207110)
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| Co-Investigator(Renkei-kenkyūsha) |
TANINO Tetsuzo 大阪大学, 工学研究科, 教授 (50125605)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 大域的最適化問題 / 逆凸制約 / 分離超平面 / 逐次近似解法 / 大域的最適化 / 逆凸計画 / 区分的分離超平面 / KKT点 / FJ点 / 分枝限定法 / 国際情報交換 |
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| Outline of Final Research Achievements |
In this study, we consider a global optimization problem (GRC) with a reverse convex constraint. For (GRC), many approximation algorithms based on outer approximation methods and branch-and-bound procedures have been proposed. However, since the volume of data necessary for executing such algorithms increases in proportion to the number of iterations, such algorithms are not effective for large scale problems. Hence, to calculate an approximate solution of a large scale (GRC), we propose new iterative solution methods. To avoid the growth of data storage, the proposed methods find an approximate solution of (GRC) by rotating a partial separating hyperplane around a convex set defining the feasible set at each iteration. Moreover, in order to improve the computational efficiency of the proposed methods, we utilize the polar coordinate system. Moreover, we apply the proposed algorithms to optimize a linear function over a weakly efficient set of a multi-objective programming problem.
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Report
(4 results)
Research Products
(29 results)
