## Large-Scale Optimization with Applications: Part III: Molecular Structure and OptimizationMany important molecular conformation problems, such as protein folding, are expressed as global minimization problems. It is the fact that local minimization is insufficient, that markedly differentiates this volume from the previous two. Unfortunately, global minimization problems that result from models of molecular conformation are usually intractable. For example, simple 1-dimensional versions of distance conformation problems are NP-hard. Nevertheless, there has been significant recent progress in the design of promising heuristic strategies (often involving the use of high- performance parallel computers) for computing approximate global minimizers. The purpose of the sessions represented in this volume was to discuss the new algorithmic advances for global minimization in the context of protein folding and related molecular minimization problems. Emphasis was on practical shortcomings of current approaches, outstanding problems and questions, and the use of high-performance parallel computers. |

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### Contents

AN ALGORITHM FOR MOLECULAR STRUCTURE PREDICTION | 1 |

POTENTIAL TRANSFORMATION METHOD FOR GLOBAL OPTIMIZATION | 23 |

MULTISPACE SEARCH FOR PROTEIN FOLDING | 47 |

MODELING THE STRUCTURE OF ICE AS A PROBLEM IN GLOBAL MINIMIZATION | 69 |

NOVEL APPLICATIONS OF OPTIMIZATION TO MOLECULE DESIGN | 73 |

ISSUES IN LARGESCALE GLOBAL MOLECULAR OPTIMIZATION | 99 |

GLOBAL MINIMIZATION OF LENNARDJONES FUNCTIONS ON TRANSPUTER NETWORKS | 123 |

VARIABLESCALE COARSEGRAINING IN MACROMOLECULAR GLOBAL OPTIMIZATION | 135 |

GLOBAL OPTIMIZATION FOR MOLECULAR CLUSTERS USING A NEW SMOOTHING APPROACH | 163 |

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### Common terms and phrases

AGDA algorithm for molecular approach Chem computational configuration coordinates defined dihedral angles distance constraints distance geometry problem effective energy evaluation find the global free-energy function value Gaussian transform genetic algorithms global minimizer global optimization algorithm gradient Hessian matrix hyperrectangle initial interactions iteration kcal/mol large number Large-Scale Optimization lattice structure Lennard Lennard-Jones clusters Lennard-Jones potential Lennard-Jones problems LJ cluster local search macrostate Mathematics matrix Met-enkephalin minimization problem minimum mization molecular conformation molecular dynamics molecular energy minimization molecule multispace search algorithm number of atoms objective function order flips original problem packet Pardalos performed Phase Phys potential energy potential energy function potential function problem instance protein folding reverse tracking scale scrambling search search method sequence SHALLOWAY simulated annealing smoothed minimizers smoothed problem smoothing functions smoothing level smoothing parameters smoothing techniques SNIFR solution solve temperature tion trajectory diagram transputer unsmoothed vector

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Page 198 - Quantum Monte Carlo study of the thermodynamic properties of argon clusters: The homogeneous nucleation of argon in argon vapor and "magic number" distributions in argon vapor.