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MULTILEVEL AND ADAPTIVE METHODS FOR NONLINEAR OPTIMIZATION PROBLEMS: From quantization to materials design (Paperback)

Maria Emelianenko

ISBN 10: 3639224361 / ISBN 13: 9783639224368
Editorial: VDM Verlag, Germany, 2010
Nuevos Condición: New Encuadernación de tapa blanda
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Language: English. Brand new Book. This work discusses some novel multilevel and adaptive methods for nonlinear non-convex optimization, focusing on two particular problems that come from the fields of materials science and quantization, with numerous applications, including image/signal compression, mesh generation and optimal placement of resources in the context of centroidal Voronoi tessellations. In particular, several acceleration methods for quantization are developed, including Newton-type and multilevel algorithms, both of which yield significant speedup comparing to traditional methods. Rigorous convergence analysis is provided and uniform convergence of the multilevel scheme with respect to the grid size and the number of grid levels is demonstrated. A new adaptive scheme for automating phase diagram construction in complex multicomponent materials systems is proposed. The new method utilizes the geometric properties of the energy surfaces together with effective sampling techniques to improve on the starting points for the minimization, which allows for a more accurate detection of miscibility gaps and more reliable materials characterization. N° de ref. de la librería KNV9783639224368

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Título: MULTILEVEL AND ADAPTIVE METHODS FOR ...

Editorial: VDM Verlag, Germany

Año de publicación: 2010

Encuadernación: Paperback

Condición del libro: New

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This work discusses some novel multilevel and adaptive methods for nonlinear non-convex optimization, focusing on two particular problems that come from the fields of materials science and quantization, with numerous applications, including image/signal compression, mesh generation and optimal placement of resources in the context of centroidal Voronoi tessellations. In particular, several acceleration methods for quantization are developed, including Newton-type and multilevel algorithms, both of which yield significant speedup comparing to traditional methods. Rigorous convergence analysis is provided and uniform convergence of the multilevel scheme with respect to the grid size and the number of grid levels is demonstrated. A new adaptive scheme for automating phase diagram construction in complex multicomponent materials systems is proposed. The new method utilizes the geometric properties of the energy surfaces together with effective sampling techniques to improve on the starting points for the minimization, which allows for a more accurate detection of miscibility gaps and more reliable materials characterization.

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