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Positive semidefinite relaxations for distance geometry problems

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Abstract

We consider distance geometry problems for determiningr-dimensional coordinates ofn 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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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, 152-8552, Tokyo, Japan

    Yasutoshi Yajima

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  1. Yasutoshi Yajima
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Correspondence to Yasutoshi Yajima.

Additional information

This research was partly supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. 13650063.

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Yajima, Y. Positive semidefinite relaxations for distance geometry problems. Japan J. Indust. Appl. Math. 19, 87–112 (2002). https://doi.org/10.1007/BF03167449

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  • DOI: https://doi.org/10.1007/BF03167449

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