Hyperbolic smoothing and penalty techniques applied to molecular structure determination

This work considers the problem of estimating the relative positions of all atoms of a protein, given a subset of all the pair-wise distances between the atoms. This problem is NP-hard, and the usual formulations are nonsmoothed and nonconvex, having a high number of local minima. Our contribution is an efficient method that combines the hyperbolic smoothing and the penalty techniques that are useful in obtaining differentiability and reducing the number of local minima.

► Computing the geometry of a protein using interatomic distances is a hard problem.
► The usual formulations are nonsmoothed and nonconvex, having many local minimizers.
► We present a continuation method that combines smoothing and penalty techniques.
► Our approach reduces the number of local minimizers.