Premium
Global optimization using bad derivatives: Derivative‐free method for molecular energy minimization
Author(s) -
Andricioaei Ioan,
Straub John E.
Publication year - 1998
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(199810)19:13<1445::aid-jcc2>3.0.co;2-q
Subject(s) - minification , energy minimization , derivative (finance) , derivative free optimization , mathematical optimization , energy (signal processing) , computer science , computational chemistry , algorithm , optimization problem , chemistry , mathematics , multi swarm optimization , statistics , economics , financial economics
A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse‐graining” transformation of the objective function, U , into a smoothed function with few minima. When the coarse‐graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, ϵ , is a simple three‐point finite difference of U . When ϵ is very large, the gradient of ϵ appears to be a “bad derivative” of U . Because the gradient of ϵ is a simple function of U , minimization on the smoothed surface requires no explicit calculation or differentiation of ϵ . The minimization method is “derivative‐free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high‐dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998