| Project/Area Number |
10450041
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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 |
Engineering fundamentals
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KONNO Hiroshi Tokyo Institute of Technology, Decision Science and Technology, Professor, 大学院・社会理工学研究科, 教授 (10015969)
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| Co-Investigator(Kenkyū-buntansha) |
UNO Takesaki Tokyo Institute of Technology, Decision Research Assistant, 大学院・社会理工学研究科, 助手 (00302977)
MIZUNO Shinji Tokyo Institute of Technology, Decision Science and Technology, Associate Professor, 大学院・社会理工学研究科, 助教授 (90174036)
YAJIMA Yasutoshi Tokyo Institute of Technology, Decision Science and Technology, Associate Professor, 大学院・社会理工学研究科, 助教授 (80231645)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥6,700,000 (Direct Cost: ¥6,700,000)
Fiscal Year 1999: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1998: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | industrial system / global optimization / non-convex quadratic programming / internationally diversified investment / non-convex programming / fractional function programming / combinatorial optimization / enumeration problems / 分数計画問題 / 組み合わせ最適化 / 大域的最適化法 / 線形分数関数の和 / 分枝限定法 / パラメトリック単体法 / ポントフォリオ理論 / 取引きコスト / 最小取引き単位 / 一般化凸剰法計画 |
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| Research Abstract |
Our results can be classified roughly to models of global optimization and non-convex programming. For the former, we proposed a large scale internationally diversified investment model that can drastically speed up solving optimal portfolio problems without. increasing numerical errors.
For the latter, we proposed efficient algorithms for solving non-convex quadratic programming, non-convex programming with objective functions which are products or sum of fractional functions. For low rank non-convex quadratic programming, we also proposed a fast algorithm obtained by combining heuristic methods and branch and cut method. These can solve problems that can not be solved in usual way.
For portfolio optimization problems with concave transaction costs and network flow problems with concave costs, we proposed fast branch and bound algorithms. These problems are very practical.
Combinatorial problems are one of non-convex programming problems. We improved several enumeration algorithms for matchings and directed or undirected spanning trees.
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