Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Numerical Optimization

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Convex Analysisの二,三の進展について

The Avogadro project has developed an advanced molecule editor and visualizer designed for cross-platform use in computational chemistry, molecular modeling, bioinformatics, materials science, and related areas. It offers flexible, high quality rendering, and a powerful plugin architecture. Typical uses include building molecular structures, formatting input files, and analyzing output of a wide variety of computational chemistry packages. By using the CML file format as its native document type, Avogadro seeks to enhance the semantic accessibility of chemical data types. The work presented here details the Avogadro library, which is a framework providing a code library and application programming interface (API) with three-dimensional visualization capabilities; and has direct applications to research and education in the fields of chemistry, physics, materials science, and biology. The Avogadro application provides a rich graphical interface using dynamically loaded plugins through the library itself. The application and library can each be extended by implementing a plugin module in C++ or Python to explore different visualization techniques, build/manipulate molecular structures, and interact with other programs. We describe some example extensions, one which uses a genetic algorithm to find stable crystal structures, and one which interfaces with the PackMol program to create packed, solvated structures for molecular dynamics simulations. The 1.0 release series of Avogadro is the main focus of the results discussed here. Avogadro offers a semantic chemical builder and platform for visualization and analysis. For users, it offers an easy-to-use builder, integrated support for downloading from common databases such as PubChem and the Protein Data Bank, extracting chemical data from a wide variety of formats, including computational chemistry output, and native, semantic support for the CML file format. For developers, it can be easily extended via a powerful plugin mechanism to support new features in organic chemistry, inorganic complexes, drug design, materials, biomolecules, and simulations. Avogadro is freely available under an open-source license from http://avogadro.openmolecules.net
 .

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Avogadro: an advanced semantic chemical editor, visualization, and analysis platform

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the system's overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules must keep safe pairwise distances. Obtaining such a molecular arrangement can be considered a packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules must be greater than some specified tolerance. We have developed a code able to pack millions of atoms, grouped in arbitrarily complex molecules, inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straightforward. In addition, different atoms belonging to the same molecule may also be restricted to different spatial regions, in such a way that more ordered molecular arrangements can be built, as micelles, lipid double-layers, etc. The packing time for state-of-the-art molecular dynamics systems varies from a few seconds to a few minutes in a personal computer. The input files are simple and currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and can be downloaded from http://www.ime.unicamp.br/~martinez/packmol/.

/pdf/packmol-a-package-for-building-initial-configurations-for-qsy9r74wrw.pdf

PACKMOL: a package for building initial configurations for molecular dynamics simulations.

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo--Lampariello--Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the one-dimensional search process. Convergence properties and extensive numerical results are presented.

/pdf/nonmonotone-spectral-projected-gradient-methods-on-convex-1tesp83age.pdf

Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Molecular Dynamics is a powerful methodology for the comprehension at molecular level of many chemical and biochemical systems. The theories and techniques developed for structural and thermodynamic analyses are well established, and many software packages are available. However, designing starting configurations for dynamics can be cumbersome. Easily generated regular lattices can be used when simple liquids or mixtures are studied. However, for complex mixtures, polymer solutions or solid adsorbed liquids (for example) this approach is inefficient, and it turns out to be very hard to obtain an adequate coordinate file. In this article, the problem of obtaining an adequate initial configuration is treated as a "packing" problem and solved by an optimization procedure. The initial configuration is chosen in such a way that the minimum distance between atoms of different molecules is greater than a fixed tolerance. The optimization uses a well-known algorithm for box-constrained minimization. Applications are given for biomolecule solvation, many-component mixtures, and interfaces. This approach can reduce the work of designing starting configurations from days or weeks to few minutes or hours, in an automated fashion. Packing optimization is also shown to be a powerful methodology for space search in docking of small ligands to proteins. This is demonstrated by docking of the thyroid hormone to its nuclear receptor.

/pdf/packing-optimization-for-automated-generation-of-complex-1nr0z0whc2.pdf

Packing optimization for automated generation of complex system's initial configurations for molecular dynamics and docking.

Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems in which the constraints are only of the lower-level type. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved using the constant positive linear dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The resolution of location problems in which many constraints of the lower-level set are nonlinear is addressed, employing the spectral projected gradient method for solving the subproblems. Problems of this type with more than $3 \times 10^6$ variables and $ 14 \times 10^6$ constraints are solved in this way, using moderate computer time. All the codes are available at http://www.ime.usp.br/$\sim$egbirgin/tango/.

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On Augmented Lagrangian Methods with General Lower-Level Constraints

A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak—Ribiere and the Fletcher—Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented.

/pdf/a-spectral-conjugate-gradient-method-for-unconstrained-56lcp166eh.pdf

José Mario Martínez

Papers

PACKMOL: a package for building initial configurations for molecular dynamics simulations.

Nonmonotone Spectral Projected Gradient Methods on Convex Sets

Packing optimization for automated generation of complex system's initial configurations for molecular dynamics and docking.

On Augmented Lagrangian Methods with General Lower-Level Constraints

A Spectral Conjugate Gradient Method for Unconstrained Optimization