Lectures on Optimization - Theory and Algorithms

Gateaux Derivatives......Page 7
Taylor's Formula......Page 13
Convexity and Gateaux Differentiability......Page 16
Gateaux Differentiability and Weak Lower.........Page 20
Commutation of Derivations......Page 21
Frechet Derivatives......Page 22
Model Problem......Page 24
Minimisation Without Convexity......Page 27
Minimistion with Convexity conditions......Page 31
Applications to the Model Problem and.........Page 35
Some Functional Spaces......Page 38
Examples......Page 41
Minimisation Without Constraints - Algorithms......Page 55
Method of Descent......Page 57
Generalized Newton's Method......Page 78
Other Methods......Page 91
Linearization Method......Page 93
Centre Method......Page 109
Method of Gradient and Prohection......Page 112
Minimization in Product Spaces......Page 116
Duality and Its Applications......Page 147
Preliminaries......Page 148
Duality in Finite Dimensional Spaces Via......Page 158
Duality in Infinite Dimensional Spaces Via.........Page 166
Minimization of Non-Differentiable Functionals.........Page 186
Optimal Control Theory......Page 197
Theory of Optimal Design......Page 216