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A Powerful Truncated Newton Method for Potential Energy Minimization

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With advances in computer architecture and software, Newton methods are
becoming not only feasible for large-scale nonlinear optimization problems,
but also reliable, fast and efficient. Truncated Newton methods, in particular,
are emerging as a versatile subclass. In this article we present a truncated
Newton algorithm specifically developed for potential energy minimization.
The method is globally convergent with local quadratic convergence. Its
key ingredients are: 1)* approximation* of the Newton direction far
away from local minima, 2) solution of the Newton equation iteratively
by the linear Conjugate Gradient method and 3) preconditioning of the Newton
equation by the analytic second-derivative components of the "local" chemical
interactions: bond length, bond angle and torsional potentials. Relaxation
of the required accuracy of the Newton search direction diverts the minimization
search away from regions where the function is nonconvex and towards physically
interesting regions. The preconditioning strategy significantly accelerates
the iterative solution for the Newton search direction, and therefore reduces
the computation time for each iteration. With algorithmic variations, the
truncated Newton method can be formulated so that storage and computational
requirements are comparable to those of the nonlinear Conjugate Gradient
method. As the convergence rate of nonlinear Conjugate Gradient methods
is linear and performance less predictable, the application of the truncated
Newton code to potential energy functions is promising.

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