Lagrange Multiplier Approach to Variational Problems and Applications
Part of Advances in Design and Control
- Authors:
- Kazufumi Ito, North Carolina State University
- Karl Kunisch, Karl-Franzens-Universität Graz, Austria
- Date Published: November 2008
- availability: Available in limited markets only
- format: Paperback
- isbn: 9780898716498
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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.
Read more- 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: Available in limited markets only
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.
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