Shapes and Geometries – Metrics, Analysis, Differential Calculus, and Optimization
Metrics, Analysis, Differential Calculus, and Optimization

Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

M. Delfour (Author), J.–p. Zolésio (Author)

9780898719369

Hardback, published 30 December 2010

645 pages
25.9 x 18.2 x 3.3 cm, 1.283 kg

A self-contained presentation of the mathematical foundations, constructions and tools necessary for studying problems where the modeling, optimization or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. This second edition presents the latest ground breaking theoretical foundation to shape optimization in a form that can used by the engineering and scientific communities. It also clearly explains the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field. The area of research is very broad, rich and fascinating from both theoretical and numerical standpoints and this book reflects this exciting expanding field. This book will be of great importance to applied mathematicians, as well as advanced engineers and scientists working in this area.

List of figures
Preface
1. Introduction: examples, background, and perspectives
2. Classical descriptions of geometries and their properties
3. Courant metrics on images of a set
4. Transformations generated by velocities
5. Metrics via characteristic functions
6. Metrics via distance functions
7. Metrics via oriented distance functions
8. Shape continuity and optimization
9. Shape and tangential differential calculuses
10. Shape gradients under a state equation constraint
Elements of bibliography
Index of notation
Index.

Subject Areas: Miscellaneous items [WZ]