| Project/Area Number |
11680441
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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, Graduate School of Information Science and Engineering, Professor, 大学院・情報理工学研究科, 教授 (90092551)
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| Co-Investigator(Kenkyū-buntansha) |
FUJISAWA Katsuki Graduate School of Engineering, Kyoto University, Research Associate, 大学院・工学研究科, 助手 (40303854)
DAI Yang Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Assistant Professor, 大学院・情報理工学研究科, 講師 (40244678)
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| Project Period (FY) |
1999 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Quadratic Optimization Problem / Linear Program / Semidefinite Program / Combinatorial Optimization / Relaxation / Complexity / 主双対内点法 |
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| Research Abstract |
In this research project, we studied a general Quadratic Optimization Problem(QOP)having a linear objective function c^Tx to be maximized over a compact subset F of the n-dimensional Euclidean space R^n represented by(finitely or infinitely many)quadratic inequalities. There are two viriants of successive convex relaxation method, the SSDP(Successive Semidefinite Programming)Relaxation Method and the SSILP(Successive Semi-Infinite Linear Programming)Relaxation Method. Each of the methods generates a sequence of compact convex subsets C_k(k=1,2, ...)of R^n which monotonically converges to the convex hull of F.To implements the SSDP and SSILP Relaxation Methods, we introduced two new techniques, "discretization " and "localization." The discretization technique makes it possible to approximate an infinite number of semi-infinite SDPs(or semi-infinite LPs)which appeared at each iteration of the original methods by a finite number of standard SDPs(or standard LPs)with a finite number of linear inequality constraints. The localization technique is for the cases where we are only interested in upper bounds on the optimal objective value(for a fixed objective function vector c)but not in a global approximation of the convex hull of F.This technique allows us to generate a convex relaxation of F that is accurate only in certain directions in a neighborhood of the objective direction c. This cuts off redundant work to make the convex relaxation accurate in unnecessary directions. Through numerical experiments, we confirmed that these two techniques worked effectively for large scale QOPs.
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