Some robust optimization methods for inverse problems.
Wang, Yiran. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. === Includes bibliographical references (leaves 70-73). === Abstract also in Chinese. === Chapter 1 --- Introduction --- p.6 === Chapter 1.1 --- Overview of the subject --- p.6 === Chapter 1.2 --- Motivation --- p.8 === Cha...
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| Format: | Others |
| Language: | English Chinese |
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2009
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| Online Access: | http://library.cuhk.edu.hk/record=b5894123 http://repository.lib.cuhk.edu.hk/en/item/cuhk-326946 |
| Summary: | Wang, Yiran. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. === Includes bibliographical references (leaves 70-73). === Abstract also in Chinese. === Chapter 1 --- Introduction --- p.6 === Chapter 1.1 --- Overview of the subject --- p.6 === Chapter 1.2 --- Motivation --- p.8 === Chapter 2 --- Inverse Medium Scattering Problem --- p.11 === Chapter 2.1 --- Mathematical Formulation --- p.11 === Chapter 2.1.1 --- Absorbing Boundary Conditions --- p.12 === Chapter 2.1.2 --- Applications --- p.14 === Chapter 2.2 --- Preliminary Results --- p.17 === Chapter 2.2.1 --- Weak Formulation --- p.17 === Chapter 2.2.2 --- About the Unique Determination --- p.21 === Chapter 3 --- Unconstrained Optimization: Steepest Decent Method --- p.25 === Chapter 3.1 --- Recursive Linearization Method Revisited --- p.25 === Chapter 3.1.1 --- Frechet differentiability --- p.26 === Chapter 3.1.2 --- Initial guess --- p.28 === Chapter 3.1.3 --- Landweber iteration --- p.30 === Chapter 3.1.4 --- Numerical Results --- p.32 === Chapter 3.2 --- Steepest Decent Analysis --- p.35 === Chapter 3.2.1 --- Single Wave Case --- p.36 === Chapter 3.2.2 --- Multiple Wave Case --- p.39 === Chapter 3.3 --- Numerical Experiments and Discussions --- p.43 === Chapter 4 --- Constrained Optimization: Augmented Lagrangian Method --- p.51 === Chapter 4.1 --- Method Review --- p.51 === Chapter 4.2 --- Problem Formulation --- p.54 === Chapter 4.3 --- First Order Optimality Condition --- p.56 === Chapter 4.4 --- Second Order Optimality Condition --- p.60 === Chapter 4.5 --- Modified Algorithm --- p.62 === Chapter 5 --- Conclusions and Future Work --- p.68 === Bibliography --- p.70 |
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