Lagrange Multiplier Approach to Variational Problems and Applications

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.

Spis treści:
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.