Modeling and Convexity

Modeling and Convexity By
2010 | 507 Pages | ISBN: 1848211775 | PDF | 6 MB
This reference book gives the reader a complete but comprehensive presentation of the foundations of convex analysis and presents applications to significant situations in engineering. The presentation of the theory is self-contained and the proof of all the essential results is given. The examples consider meaningful situations such as the modeling of curvilinear structures, the motion of a mass of people or the solidification of a material. Non convex situations are considered by means of relaxation methods and the connections between probability and convexity are explored and exploited in order to generate numerical algorithms.Content: Chapter 1 Curvilinear Continuous Media (pages 1-32): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 2 Unilateral System Dynamics (pages 33-52): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 3 A Simplified Model of Fusion/Solidification (pages 53-60): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 4 Minimization of a Non?Convex Function (pages 61-68): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 5 Simple Models of Plasticity (pages 69-76): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 6 Elements of Set Theory (pages 77-96): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 7 Real Hilbert Spaces (pages 97-200): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 8 Convex Sets (pages 201-252): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 9 Functionals on a Hilbert Space (pages 253-360): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 10 Optimization (pages 361-420): Eduardo Souza de Cursi, Rubens Sampaio and Piotr BreitkopfChapter 11 Variational Problems (pages 421-486): Eduardo Souza de Cursi, Rubens Sampaio and Piotr Breitkopf