Solving Large Scale Molecular Distance Geometry Problems by a Smoothing Technique via the Gaussian Transform and D.C. Programming

We study a continuation approach via the Gaussian transform and D.C. programming for solving both exact and general distance geometry problems. This approach relies on a new formulation of the problems and their Gaussian transforms which are both smooth D.C. (difference of convex functions) programs. A D.C. optimization algorithm is investigated for solving the transformed problems. Numerical experiments on the data derived from PDB data bank up to 4189 atoms show the usefulness of the reformulation, the globality of sought solutions, the robustness and the efficiency of the proposed approach.

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