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Lagrange Multiplier Approach to Variational Problems and Applications

Lagrange Multiplier Approach to Variational Problems and Applications

£80.00

Part of Advances in Design and Control

  • Date Published: November 2008
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716498

£ 80.00
Paperback

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About the Authors
  • This comprehensive monograph analyses Lagrange multiplier theory, which provides a tool for the analysis of a general class of nonlinear variational problems, and is the basis for developing efficient and powerful iterative methods for solving these problems. This book shows its impact on the development of numerical algorithms for problems posed in a function space setting, and is motivated by the idea that a full treatment of a variational problem in function spaces would be incomplete without a discussion of infinite-dimensional analysis, proper discretisation, and the relationship between the two. The authors develop and analyse efficient algorithms for constrained optimisation and convex optimisation problems based on the augmented Lagrangian concept and cover such topics as sensitivity analysis and convex optimisation. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black–Scholes model.

    • For researchers in optimisation and control theory, numerical PDEs, and applied analysis
    • Also suitable for advanced graduate students in applied analysis and PDE optimisation
    • Applies general theory to a variety of challenging problems
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    Product details

    • Date Published: November 2008
    • format: Paperback
    • isbn: 9780898716498
    • length: 360 pages
    • dimensions: 255 x 179 x 19 mm
    • weight: 0.66kg
    • 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

    Preface
    1. Existence of Lagrange multipliers
    2. Sensitivity analysis
    3. First Order augmented Lagrangians for equality and finite rank inequality constraints
    4. Augmented Lagrangian methods for nonsmooth, convex optimization
    5. Newton and SQP methods
    6. Augmented Lagrangian-SQP methods
    7. The primal-dual active set method
    8. Semismooth Newton methods I
    9. Semismooth Newton methods II: applications
    10. Parabolic variational inequalities
    11. Shape optimization
    Bibliography
    Index.

  • Authors

    Kazufumi Ito, North Carolina State University
    Kazufumi Ito is Professor in the Department of Mathematics and an affiliate of the Center for Research in Scientific Computation at North Carolina State University. He was co-recipient of the SIAM Outstanding Paper Award in 2006.

    Karl Kunisch, Karl-Franzens-Universität Graz, Austria
    Karl Kunisch is Professor in the Institute of Mathematics at the University of Graz, Austria. He was co-recipient of the SIAM Outstanding Paper Award in 2006.

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