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Large scale molecular conformation via the exact distance geometry problem. (English) Zbl 0982.90037
Nguyen, Van Hien (ed.) et al., Optimization. Proceedings of the 9th Belgian-French-German conference, Namur, Belgium, September 7-11, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 481, 260-277 (2000).
Summary: We develop in this paper a method based on a d.c. (difference of convex functions) optimization approach called DCA for solving large-scale exact distance geometry problem. Requiring only matrix-vector products and one Cholesky factorization, the DCA seems to be robust and efficient in large scale problems. Moreover it allows exploiting sparsity of the given distance matrix. A technique using the triangle inequality to generate a complete approximate distance matrix was investigated in order to compute a good starting point for the DCA. Numerical simulations of the molecular conformation problems with up to 12288 variables are reported that prove the robustness, the efficiency, and the globality of our algorithms.
For the entire collection see [Zbl 0935.00054].

90C26 Nonconvex programming, global optimization