2002 Fiscal Year Final Research Report Summary
New Methods for Distance Geometry Problems
| Project/Area Number |
13650063
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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 |
Engineering fundamentals
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
YAJIMA Yasutoshi Tokyo Institute of Technology, Graduate School of 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) |
2001 – 2002
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| Keywords | Distance Geometry / Molecular Conformation / Positive Semidefinite Programming / 大域的最適化 / 非凸2次計画問題 |
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| Research Abstract |
We consider distance geometry problems for determining $r$--dimensional coordinates of $n$ points from a given set of the distances between the points. This problem is a fundamental problem in molecular biology for finding the structure of proteins from NMR (Nuclear Magnetic Resonance) data.
We formulate the problem as the minimization of an error function defined by the sum of the absolute differences, which is a typical nonconvex optimization problem. We show that this problem can be reduced into a concave quadratic minimization problem. We propose positive semidefinite relaxations as well as local search procedures for this problem. Our numerical results show that we can generate acceptable solutions of the problem with up to 800 points.
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