New Methods for Distance Geometry Problems

距离几何问题的新方法

• 批准号: 13650063
• 负责人: YAJIMA Yasutoshi
• 金额: $ 2.11万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650063/
• 关键词: Distance Geometry; Molecular Conformation; Positive Semidefinite Programming; 大域的最適化; 非凸2次計画問題; 半正定値計画; 大域的的最適化

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.

我们考虑距离几何问题，用于根据给定的一组点之间的距离确定 $r$——$n$ 个点的维坐标。该问题是分子生物学中从NMR（核磁共振）数据中寻找蛋白质结构的一个基本问题。我们将该问题表述为由绝对差之和定义的误差函数的最小化，这是典型的非凸优化问题。我们证明这个问题可以简化为凹二次最小化问题。我们针对这个问题提出了正半定松弛以及局部搜索程序。我们的数值结果表明，我们可以生成最多 800 个点的可接受的问题解决方案。