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Multivariate Minimization in Computational Chemistry

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Molecular Modeling and Simulation: An Interdisciplinary Guide

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 21))

Abstract

Optimization is a fundamental component of molecular modeling. The determination of a low-energy conformation for a given force field can be the final objective of the computation. It can also serve as a starting point for subsequent calculations, such as molecular dynamics simulations or normal-mode analyses.

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Notes

  1. 1.

    The notorious ‘traveling salesman’ problem seeks to find the optimal travel route that covers a given number of cities, each one only once, and returning to the home town. Visually, imagine drawing such a route on a map, where each city k for k = 0, …, n is designated by coordinates {x k , y k }. The connected route started at {x 0, y 0} covers each city and returns to the original point. Though simple to envision, there are clearly many such routes, and the number of combinations that connect all these cities grows steeply with n. This problem in fact belongs to a class of very difficult problems (known as NP-complete)for which no polynomial-complexity algorithm is known (i.e., the computational time for an exact solution of this problem increases exponentially with n).

  2. 2.

    This does not imply that the reduction in the gradient norm is monotonic; see Figure 11.11 for example.

  3. 3.

    Typically, ε m is 10− 15 and 10− 7, respectively, for double and single-precision IEEE arithmetic [954].

  4. 4.

    See historical note below on the method’s name.

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  1. Courant Institute of Mathematical Sciences and Department of Chemistry, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Prof. Tamar Schlick

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Schlick, T. (2010). Multivariate Minimization in Computational Chemistry. In: Molecular Modeling and Simulation: An Interdisciplinary Guide. Interdisciplinary Applied Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6351-2_11

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