© 2014

Functional Analysis and Applied Optimization in Banach Spaces

Applications to Non-Convex Variational Models


Table of contents

  1. Front Matter
    Pages i-xviii
  2. Basic Functional Analysis

    1. Front Matter
      Pages 1-1
    2. Fabio Botelho
      Pages 3-40
    3. Fabio Botelho
      Pages 57-97
    4. Fabio Botelho
      Pages 99-128
    5. Fabio Botelho
      Pages 129-146
    6. Fabio Botelho
      Pages 147-166
    7. Fabio Botelho
      Pages 167-174
    8. Fabio Botelho
      Pages 175-221
  3. Variational Convex Analysis

    1. Front Matter
      Pages 223-223
    2. Fabio Botelho
      Pages 225-249
    3. Fabio Botelho
      Pages 251-285
    4. Fabio Botelho
      Pages 287-317
  4. Applications

    1. Front Matter
      Pages 319-319
    2. Fabio Botelho
      Pages 321-341
    3. Fabio Botelho
      Pages 343-362
    4. Fabio Botelho
      Pages 373-392

About this book


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.


applied optimization calculus of variations duality functional analysis variational convex analysis

Authors and affiliations

  1. 1.Department of Mathematics and StatisticsFederal University of PelotasPelotasBrazil

Bibliographic information

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“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)