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

• Authors: Zhijun Wu
• Venue: The Effective Energy Transformation Scheme as a General Continuation Approach to Global Optimization with Application to Molecular Conformation
• Year: 1993

This paper discusses a generalization of the special function transformation scheme for global minimization for molecular conformation used in [3,4,14,15]. Theories for the method as a general continuation approach are established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but "smoother", functions. An optimization procedure can then be applied to the new functions successively, to trace the solution back to the original function. Two types of transformation are defined: the isotropic and the anisotropic. We show that both, although not applicable numerically to arbitrary functions because of the required high dimensional integration, can be applied to a large class of nonlinear partially separable functions, and, in particular, the energy functions for molecular conformation. Methods to compute exactly the required transformations are given. Advantages of this transformation approach over the conventional homotopy methods also are discussed. Keywords: global/local minimization, continuation methods, integral transformation, molecular conformation