The Eeective Energy Transformation Scheme as a General 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.

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