By K. A. Dill, A. T. Phillips, J. B. Rosen (auth.), Lorenz T. Biegler, Andrew R. Conn, Thomas F. Coleman, Fadil N. Santosa (eds.)
Many very important molecular conformation difficulties, similar to protein folding, are expressed as international minimization difficulties. it's the proven fact that neighborhood minimization is inadequate, that markedly differentiates this quantity from the former . regrettably, worldwide minimization difficulties that outcome from versions of molecular conformation tend to be intractable. for instance, easy 1-dimensional types of distance conformation difficulties are NP-hard. however, there was major contemporary development within the layout of promising heuristic suggestions (often related to using excessive- functionality parallel desktops) for computing approximate worldwide minimizers. the aim of the classes represented during this quantity was once to debate the recent algorithmic advances for worldwide minimization within the context of protein folding and similar molecular minimization difficulties. Emphasis used to be on useful shortcomings of present techniques, notable difficulties and questions, and using high-performance parallel computers.
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Additional info for Large-Scale Optimization with Applications: Part III: Molecular Structure and Optimization
Example text
9 1. 9 1. 1. 08 40 ROBERT A. DONNELLY ing of minima). Reducing f too much has the effect of reducing sensitivity of the dynamics to the local gradient Finally we should point out that these results were obtained by treating the objective function more or less as a "black box," in the sense that no special methods were followed which exploited the special nature of this problem. We would not argue that this is the correct approach to follow in solving a "real" problem. We would argue, however, that such success rates following an uneducated starting point speaks well for the efficacy of the potential transform method.
Part of Trajectory SII 250 300 Step POTENTIAL TRANSFORM METHODS FOR GLOBAL OPTIMIZATION 33 Speed PT Speeds 120 100 80 ," , 60 40 20 / ,, , , ,/ ," , ," ,, " ", " ... ------' .... " ---------1 " / " " ,, ,, \ \ \\ \\ \ \ , / 100 \ 150 200 250 300 \ \ \ \ , \ f FIG. 4. Speed u(J) form, where it remained trapped for the duration of its run. In fact it is just such behavior of SNIFR which caused us to reexamine its theoretical underpinning, leading to our derivation of the PT equations! In both series PT made some large uphill moves and found the basis of attraction of the chair with relative ease.
Problem 1: Molecular conformations. We begin our evaluation of the PT method with a pedagogical problem illustrating one application of minimization methods to chemistry, namely search for the molecular conformation which is also the global energy minimum. The term "molecular conformation" refers to different arrangements of atoms produced by rotation about chemical bonds: a change in conformation does not involve breaking chemical bonds. Mathematically speaking, "conformations" are stationary points on a potential energy surf~ce at which the potential en~ ergy is a (local) minimum.