Functional Analysis and Applied Optimization in Banach Spaces

Download or read book Functional Analysis and Applied Optimization in Banach Spaces written by Fabio Botelho and published by Springer. This book was released on 2014-06-12 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​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.