# Modeling and Convexity

ISBN: 9781848211773

Publication Date: May 2010 Hardback 528 pp.

215.00 USD

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Description

This reference book gives to 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.

Contents

PART 1. MOTIVATION: EXAMPLES AND APPLICATIONS

1. Curvilinear Continuous Media.

2. Unilateral System Dynamics.

3. A Simplified Model of Fusion/Solidification.

4. Minimization of a Non-Convex Function.

5. Simple Models of Plasticity.

PART 2. THEORETICAL ELEMENTS

6. Elements of Set Theory.

7. Real Hilbert Spaces.

8. Convex Sets.

9. Functionals on a Hilbert Space.

10. Optimization.

11. Variational Problems.

About the Authors

Eduardo Souza de Cursi is Professor, Director of European and International Relations and Director of the Laboratory of Mechanics at INSA-Rouen in France.

Rubens Sampaio is Professor at PUC-Rio, Rio de Janeiro, Brazil. His fields of interest are Applied Mathematics and Mechanics.

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