Optimization approaches for some nonlinear inverse problems.

Keung Yee Lo. ; Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. ; Includes bibliographical references (leaves 109-111). ; Chapter 1 --- Introduction --- p.1 ; Chapter 1.1 --- Inverse problems and Parameter Identification --- p.1 ; Chapter 1.2 --- Examples in inverse problems --- p.2 ; Chapter 1.3 --- Applications in parameter identifications --- p.5 ; Chapter 1.4 --- Difficulties arising in inverse problems --- p.7 ; Chapter 2 --- Identifying Parameters in Parabolic Systems --- p.9 ; Chapter 2.1 --- Introduction --- p.9 ; Chapter 2.2 --- An averaging-terminal status formulation and existence of its solutions --- p.12 ; Chapter 2.3 --- Optimization approach and its convergence --- p.17 ; Chapter 2.4 --- Unconstrained minimization problems --- p.26 ; Chapter 2.5 --- Armijo algorithm --- p.28 ; Chapter 2.6 --- Numerical experiments --- p.32 ; Chapter 2.6.1 --- Convergence of the minimization problem --- p.40 ; Chapter 2.7 --- Noisy data --- p.59 ; Chapter 3 --- Identifying Parameters in Elliptic Systems --- p.68 ; Chapter 3.1 --- Augmented Lagrangian Method --- p.68 ; Chapter 3.2 --- The discrete saddle-point problem --- p.70 ; Chapter 3.3 --- An Uzawa algorithm --- p.71 ; Chapter 3.4 --- Formulation of the algorithm --- p.73 ; Chapter 3.5 --- Numerical experiments --- p.76 ; Chapter 3.6 --- Alternative formulation of the cost functional --- p.90 ; Chapter 3.7 --- Iterative GMRES method --- p.102 ; Bibliography --- p.109