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

Fabio Botelho

ISBN 10: 3319382063 / ISBN 13: 9783319382067

Editore: Springer International Publishing, Springer International Publishing, 2016

Riguardo questo articolo

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 9783319382067

Dati bibliografici

Titolo: Functional Analysis and Applied Optimization...

Casa editrice: Springer International Publishing, Springer International Publishing

Data di pubblicazione: 2016

Legatura: Taschenbuch

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.

Recensione:

“The aim of the present book is to consider a variety of problems arising in applications in relation with non-convex variational models. ... The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics, and engineering.” (Ján Lovíšek, Mathematical Reviews, August, 2015)