A stable, rapidly converging conjugate gradient method for energy minimization

We apply Shanno's conjugate gradient algorithm to the problem of minimizing the potential energy function associated with molecular mechanical calculations. Shanno's algorithm is stable with respect to roundoff errors and inexact line searches and converges rapidly to a minimum. Equally important, this algorithm can improve the rate of convergence to a minimum by a factor of 5 relative to Fletcher‐Reeves or Polak‐Ribière minimizers when used within the molecular mechanics package AMBER. Comparable improvements are found for a limited number of simulations when the Polak‐Ribière direction vector is incorporated into the Shanno algorithm.

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