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Full Description
Lagrange multiplier theory 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 comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The book is motivated by the idea that a full treatment of a variational problem in function spaces would not be complete without a discussion of in?nite-dimensional analysis, proper discretization, and the relationship between the two.
The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. 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.
Contents
Preface
Chapter 1. Existence of Lagrange Multipliers
Chapter 2. Sensitivity Analysis
Chapter 3. First Order Augmented Lagrangians for Equality and Finite Rank Inequality Constraints
Chapter 4. Augmented Lagrangian Methods for Nonsmooth, Convex Optimization
Chapter 5. Newton and SQP Methods
Chapter 6. Augmented Lagrangian-SQP Methods
Chapter 7. The Primal-Dual Active Set Method
Chapter 8. Semismooth Newton Methods I
Chapter 9. Semismooth Newton Methods II: Applications
Chapter 10. Parabolic Variational Inequalities
Chapter 11. Shape Optimization
Bibliography
Index
