Global Continuation for Distance Geometry Problems

Abstract

Distance geometry problems arise in the determination of protein structure. We consider the case where only a subset of the distances between atoms is given and formulate this distance geometry problem as a global minimization problem with special structure. We show that global smoothing techniques and a continuation approach for global optimization can be used to determine global solutions of this problem reliably and efficiently. The global continuation approach determines a global solution with less computational effort than is required by a standard multistart algorithm. Moreover, the continuation approach usually finds the global solution from any given starting point, while the multistart algorithm tends to fail.