Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models

Fabio Botelho

ISBN 10: 3319060732 / ISBN 13: 9783319060736

Editore: Springer International Publishing, 2014

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Druck auf Anfrage Neuware - Printed after ordering - This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Codice articolo 9783319060736

Dati bibliografici

• Titolo: Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models
• Editore: Springer International Publishing
• Data di pubblicazione: 2014
• Lingua: Inglese
• ISBN 10: 3319060732
• ISBN 13: 9783319060736
• Rilegatura: Buch
• Condizione: Neu

Descrizione articolo

Riassunto

?This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.