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 used in Coleman, Shalloway, and Wu [Comput. Optim. Appl., 2 (1993), pp. 145–170; J. Global Optim., 4 (1994), pp. 171–185] and Shalloway [Global Optimization, C. Floudas and P. Pardalos, eds., Princeton University Press, 1992, pp. 433–477; Global Optim., 2 (1992), pp. 281–311] for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global optimization is established. We show that the method can transform a nonlinear objective function into a class of gradually deformed, but “smoother” or “easier” functions. An optimization procedure can then be successively applied to the new functions to trace their solutions back to the original function. Two 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.