Abstract

We show that a continuation approach to global optimization with global smoothing techniques can be used to obtain "-optimal solutions to distance geometry problems. We show that determining an "-optimal solution is still an NP-hard problem when " is small. A discrete form of the Gaussian transform is proposed based on the Hermite form of Gaussian quadrature. We show that the modified transform can be used whenever the transformed functions cannot be computed analytically. Our numerical results show that the discrete Gauss transform can be used to obtain "-optimal solutions for general distance geometry problems, and in particular, to determine the three-dimensional structure of protein fragments.

Citations