The Effective Energy Transformation Scheme as a Special Continuation Approach to Global Optimization with Application to Molecular Conformation

This paper discusses a generalization of the function transformation scheme for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global o p timization is established. We show that the method can transform a nonlinear objective function into a class of &dua l ly deformed, but “smoother” or “easier“ functions. An optimization procedure can then be applied to the new functions successively, to trace their solutions back to the original function. T w o types of transformation are defined: isotropic and anisotropic. We show that both transformations can be applied to a large class of nonlinear partially separable functions including energy functions for molecular conformation. Methods to compute the transformation for these functions are given. . Abbreviated title: A Continuation Approach to Global Optimization