| Project/Area Number |
03832017
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
社会システム工学
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KOJIMA Masakazu Tokyo Institute of Technology Faculty of Science, Professor, 理学部, 教授 (90092551)
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| Co-Investigator(Kenkyū-buntansha) |
KUNO Takahito University of Tsukuba Institute of Information Sciences and Electronics Assistan, 電子情報系, 講師 (00205113)
MIZUNO Shinji The Institute of Statistical Mathematics Department of Prediction and Control As, 予測制御研究系, 助教授 (90174036)
YAJIMA Yasutoshi Tokyo Institute of Technology Faculty of Engineering Assistant Professor, 工学部, 助手 (80231645)
TAMURA Akihisa Tokyo Institute of Technology Faculty of Science, Assistant Professor, 理学部, 助手 (50217189)
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| Project Period (FY) |
1991 – 1992
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| Project Status |
Completed (Fiscal Year 1992)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1992: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1991: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Linear Program / Interior Point Method / Karmarkar's Method / Mathematical Program / Combinatorial Optimization / カ-マ-カ-法 |
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| Research Abstract |
The purpose of this study is as follow.
(1) Evaluation of complexity of primal-dual interior point algorithms for linear programs.
(2) Applications of interior point algorithms to nonconvex quadratic programs and combinatorial optimization problems.
(3) Development of software for linear programs with the use of interior point algorithms.
(4) Extension of interior point algorithms to general convex programs.
For the purpose (1), we proposed a method for controlling step lengths and a method for choosing an initial point from which an interior point for a linear program starts. We confirmed for the purpose (3) the effectiveness and efficiency of these new methods in computational experiments. We made investigation into nonconvex quadratic programs and combinatorial optimization problems, but we have not succeeded in incorporating interior point algorithms into the problems. We also extended the methods mentioned above in the purpose (1) to general convex programs.
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