Numerical optimal control in cancer chemotherapy.
by Leung Wing Chung. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. === Includes bibliographical references (leaves 67-68). === Abstract also in Chinese. === Chapter 1 --- Background and Modelling --- p.5 === Chapter 1.1 --- Treatment of Cancer --- p.5 === Chapter 1.2 --- Tumour Grow...
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| Format: | Others |
| Language: | English Chinese |
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1998
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| Online Access: | http://library.cuhk.edu.hk/record=b5896303 http://repository.lib.cuhk.edu.hk/en/item/cuhk-322272 |
| Summary: | by Leung Wing Chung. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. === Includes bibliographical references (leaves 67-68). === Abstract also in Chinese. === Chapter 1 --- Background and Modelling --- p.5 === Chapter 1.1 --- Treatment of Cancer --- p.5 === Chapter 1.2 --- Tumour Growth Model ´ؤ Gompertz Model --- p.5 === Chapter 1.3 --- Drug Concentration and Drug Effects --- p.7 === Chapter 1.3.1 --- Drug Effects on Tumour Cells --- p.9 === Chapter 1.3.2 --- "Drug Effects with Different Values of λG,k, vth" --- p.9 === Chapter 1.4 --- Constraints on the Gompertz Model --- p.11 === Chapter 2 --- Minimization on the Gompertz Model --- p.12 === Chapter 2.1 --- Mathematical Modelling on the Gompertz Model --- p.12 === Chapter 2.1.1 --- Constraints Transformation --- p.13 === Chapter 2.2 --- Simplified Minimization Problem --- p.15 === Chapter 2.2.1 --- Avoiding Non-Minimal Stationary Points --- p.16 === Chapter 2.2.2 --- The Final Minimization Problem --- p.23 === Chapter 2.2.3 --- Existence of Optimal Solutions --- p.24 === Chapter 2.3 --- Gradients of the Objective Function and the Constraints --- p.25 === Chapter 2.3.1 --- First Derivatives --- p.25 === Chapter 2.3.2 --- Second Derivatives --- p.29 === Chapter 3 --- Numerical Methods for Minimization Problems --- p.31 === Chapter 3.1 --- Lagrangian Multiplier Method --- p.32 === Chapter 3.1.1 --- Kuhn-Tucker Condition --- p.33 === Chapter 3.1.2 --- Model Augmented Lagrangian Algorithm --- p.34 === Chapter 3.1.3 --- Armijo Algorithm --- p.36 === Chapter 3.1.4 --- Modified Augmented Lagrangian Algorithm --- p.40 === Chapter 3.2 --- Data on the Gompertz Model --- p.42 === Chapter 3.2.1 --- Optimality of Solutions --- p.42 === Chapter 3.3 --- Numerical Results --- p.45 === Chapter 3.4 --- Well-Conditioned Penalty Function Method for Constrained Optimization --- p.56 === Chapter 3.5 --- Discussion --- p.64 === Chapter 3.5.1 --- Model Augmented Lagrangian Algorithm and Modified Augmented Lagrangian Algorithm --- p.65 === Chapter 3.5.2 --- Modified Augmented Lagrangian Algorithm and Penalty Function Algorithm --- p.65 === Bibliography |
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