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Shapes and Geometries

Shapes and Geometries
Analysis, Differential Calculus, and Optimization

Part of Advances in Design and Control

  • Date Published: June 2001
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898714890


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About the Authors
  • This book provides 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. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. 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.

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    Product details

    • Date Published: June 2001
    • format: Hardback
    • isbn: 9780898714890
    • length: 499 pages
    • dimensions: 260 x 182 x 27 mm
    • weight: 1.085kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    List of Figures
    1. Introduction
    2. Classical Descriptions and Properties of Domains
    3. Relaxation to Measurable Domains
    4. Topologies Generated by Distance Functions
    5. Oriented Distance Function and Smoothness of Sets
    6. Optimization of Shape Functions
    7. Transformations versus Flows of Velocities
    8. Shape Derivatives and Calculus, and Tangential Differential Calculus
    9. Shape Gradients under a State Equation Constraint
    Elements of Bibliography
    Index of Notation

  • Authors

    M. C. Delfour, Université de Montréal

    J.-P. Zolésio

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