by Chung Shun Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 158-170). / Abstracts in English and Chinese. / List of Figures --- p.x / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background and Historical Development --- p.1 / Chapter 1.2 --- Practical Problems --- p.3 / Chapter 1.2.1 --- Statistics --- p.3 / Chapter 1.2.2 --- Aerodynamics --- p.4 / Chapter 1.2.3 --- Factory Allocation Problem --- p.5 / Chapter 1.2.4 --- Parameter Problem --- p.5 / Chapter 1.2.5 --- Chemical Engineering --- p.5 / Chapter 1.2.6 --- Operational Research --- p.6 / Chapter 1.2.7 --- Economics --- p.6 / Chapter 1.3 --- Mathematical Models for Optimization Problems --- p.6 / Chapter 1.4 --- Unconstrained Optimization Techniques --- p.8 / Chapter 1.4.1 --- Direct Method - Differential Calculus --- p.8 / Chapter 1.4.2 --- Iterative Methods --- p.10 / Chapter 1.5 --- Main Objectives of the Thesis --- p.11 / Chapter 2 --- Basic Concepts in Optimizations of Smooth Func- tions --- p.14 / Chapter 2.1 --- Notation --- p.14 / Chapter 2.2 --- Different Types of Minimizer --- p.16 / Chapter 2.3 --- Necessary and Sufficient Conditions for Optimality --- p.18 / Chapter 2.4 --- Quadratic Functions --- p.22 / Chapter 2.5 --- Convex Functions --- p.24 / Chapter 2.6 --- "Existence, Uniqueness and Stability of a Minimum" --- p.29 / Chapter 2.6.1 --- Existence of a Minimum --- p.29 / Chapter 2.6.2 --- Uniqueness of a Minimum --- p.30 / Chapter 2.6.3 --- Stability of a Minimum --- p.31 / Chapter 2.7 --- Types of Convergence --- p.34 / Chapter 2.8 --- Minimization of Functionals --- p.35 / Chapter 3 --- Steepest Descent Method --- p.37 / Chapter 3.1 --- Background --- p.37 / Chapter 3.2 --- Line Search Method and the Armijo Rule --- p.39 / Chapter 3.3 --- Steplength Control with Polynomial Models --- p.43 / Chapter 3.3.1 --- Quadratic Polynomial Model --- p.43 / Chapter 3.3.2 --- Safeguarding --- p.45 / Chapter 3.3.3 --- Cubic Polynomial Model --- p.46 / Chapter 3.3.4 --- General Line Search Strategy --- p.49 / Chapter 3.3.5 --- Algorithm of Steepest Descent Method --- p.51 / Chapter 3.4 --- Advantages of the Armijo Rule --- p.54 / Chapter 3.5 --- Convergence Analysis --- p.56 / Chapter 4 --- Iterative Methods Using Second Derivatives --- p.63 / Chapter 4.1 --- Background --- p.63 / Chapter 4.2 --- Newton's Method --- p.64 / Chapter 4.2.1 --- Basic Concepts --- p.64 / Chapter 4.2.2 --- Convergence Analysis of Newton's Method --- p.65 / Chapter 4.2.3 --- Newton's Method with Steplength --- p.69 / Chapter 4.2.4 --- Convergence Analysis of Newton's Method with Step-length --- p.70 / Chapter 4.3 --- Greenstadt's Method --- p.72 / Chapter 4.4 --- Marquardt-Levenberg Method --- p.74 / Chapter 4.5 --- Fiacco and McComick Method --- p.76 / Chapter 4.6 --- Matthews and Davies Method --- p.79 / Chapter 4.7 --- Numerically Stable Modified Newton's Method --- p.80 / Chapter 4.8 --- The Role of the Second Derivative Methods --- p.89 / Chapter 5 --- Multi-step Methods --- p.92 / Chapter 5.1 --- Background --- p.93 / Chapter 5.2 --- Heavy Ball Method --- p.94 / Chapter 5.3 --- Conjugate Gradient Method --- p.99 / Chapter 5.3.1 --- Some Types of Conjugate Gradient Method --- p.99 / Chapter 5.3.2 --- Convergence Analysis of Conjugate Gradient Method --- p.108 / Chapter 5.4 --- Methods of Variable Metric and Methods of Conju- gate Directions --- p.111 / Chapter 5.5 --- Other Approaches for Constructing the First-order Methods --- p.116 / Chapter 6 --- Quasi-Newton Methods --- p.121 / Chapter 6.1 --- Disadvantages of Newton's Method --- p.122 / Chapter 6.2 --- General Idea of Quasi-Newton Method --- p.124 / Chapter 6.2.1 --- Quasi-Newton Methods --- p.124 / Chapter 6.2.2 --- Convergence of Quasi-Newton Methods --- p.129 / Chapter 6.3 --- Properties of Quasi-Newton Methods --- p.131 / Chapter 6.4 --- Some Particular Algorithms for Quasi-Newton Methods --- p.137 / Chapter 6.4.1 --- Single-Rank Algorithms --- p.137 / Chapter 6.4.2 --- Double-Rank Algorithms --- p.144 / Chapter 6.4.3 --- Other Applications --- p.149 / Chapter 6.5 --- Conclusion --- p.152 / Chapter 7 --- Choice of Methods in Optimization Problems --- p.154 / Chapter 7.1 --- Choice of Methods --- p.154 / Chapter 7.2 --- Conclusion --- p.157 / Bibliography --- p.158

Pong Ting Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 79-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Notations --- p.7 / Chapter 2.3 --- On properties of Normal Cones --- p.9 / Chapter 2.4 --- Polar Calculus --- p.13 / Chapter 2.5 --- Notions of Relative Interior --- p.17 / Chapter 2.6 --- Properties of Minkowski functional --- p.18 / Chapter 2.7 --- Properties of Epigraphs --- p.19 / Chapter 3 --- The Strong Conical Hull Intersection Property (Strong CHIP): Definition and Some Properties --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Definition of the strong CHIP --- p.24 / Chapter 3.3 --- Relationship between the strong CHIP and projections onto sets --- p.26 / Chapter 3.4 --- Relationship between the strong CHIP and the Basic Constraint Qualifications (BCQ) --- p.35 / Chapter 3.5 --- The strong CHIP of extremal subsets --- p.42 / Chapter 4 --- Sufficient Conditions for the Strong CHIP --- p.46 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- ̐ưجI̐ưجis finite --- p.47 / Chapter 4.2.1 --- Interior point conditions --- p.47 / Chapter 4.2.2 --- Boundedly linear regularity --- p.52 / Chapter 4.2.3 --- Epi-sum --- p.54 / Chapter 4.3 --- ̐ưجI̐ưجis infinite --- p.56 / Chapter 4.3.1 --- A Sum Rule --- p.57 / Chapter 4.3.2 --- The C-Extended Minkowski Functional --- p.58 / Chapter 4.3.3 --- Relative Interior Point Conditions --- p.62 / Chapter 4.3.4 --- Bounded Linear Regularity --- p.68 / Chapter 5 --- "The SECQ, Linear Regularity and the Strong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces" --- p.69 / Chapter 5.1 --- Introduction --- p.69 / Chapter 5.2 --- The strong CHIP and the SECQ --- p.71 / Chapter 5.3 --- Linear regularity and the SECQ --- p.73 / Chapter 5.4 --- Interior-point conditions and the SECQ --- p.76 / Bibliography --- p.79

by Cheng Tak Wai, Johnny. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.7 / Chapter 2.1 --- Self-dual embedding --- p.7 / Chapter 2.2 --- Conic optimization --- p.8 / Chapter 2.3 --- Self-dual embedded conic optimization --- p.9 / Chapter 2.4 --- Connection with convex programming --- p.11 / Chapter 2.5 --- Chapter summary --- p.15 / Chapter 3 --- Implementation of the algorithm --- p.17 / Chapter 3.1 --- The new search direction --- p.17 / Chapter 3.2 --- Select the step-length --- p.23 / Chapter 3.3 --- The multi-constraint case --- p.25 / Chapter 3.4 --- Chapter summary --- p.32 / Chapter 4 --- Numerical results on randomly generated problem --- p.34 / Chapter 4.1 --- Single-constraint problems --- p.35 / Chapter 4.2 --- Multi-constraint problems --- p.36 / Chapter 4.3 --- Running time and the size of the problem --- p.39 / Chapter 4.4 --- Chapter summary --- p.42 / Chapter 5 --- Geometric optimization --- p.45 / Chapter 5.1 --- Geometric programming --- p.45 / Chapter 5.1.1 --- Monomials and posynomials --- p.45 / Chapter 5.1.2 --- Geometric programming --- p.46 / Chapter 5.1.3 --- Geometric program in convex form --- p.47 / Chapter 5.2 --- Conic transformation --- p.48 / Chapter 5.3 --- Computational results of geometric optimization problem --- p.50 / Chapter 5.4 --- Chapter summary --- p.55 / Chapter 6 --- Conclusion --- p.57

Lee Sum Wai = 應用多目標基因演算法於合併三維破裂物件 / 李芯慧. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references. / Text in English; abstracts in English and Chinese. / Lee Sum Wai = Ying yong duo mu biao ji yin yan suan fa yu he bing san wei po lie wu jian / Li Xinhui. / Contents --- p.VI / List of Figures --- p.IX / List of Tables --- p.XIII / Chapter Chapter 1 --- Introduction --- p.1-1 / Chapter 1.1. --- A review of assembling objects --- p.1-3 / Chapter 1.1.1. --- Two-Dimensional matching --- p.1-3 / Chapter 1.1.2. --- Three-Dimensional matching --- p.1-4 / Chapter 1.1.3. --- 2.5-Dimensional matching --- p.1-5 / Chapter 1.2. --- Objectives of this research work --- p.1-7 / Chapter 1.2.1. --- Local Matching of fragments --- p.1-7 / Chapter 1.2.2. --- Global Matching fragments --- p.1-8 / Chapter 1.3. --- Thesis Outline --- p.1-9 / Chapter Chapter 2 --- Background Information --- p.2-1 / Chapter 2.1. --- Three-Dimensional Objects Representation --- p.2-1 / Chapter 2.2. --- Three-Dimensional Objects Geometric Transformation --- p.2-3 / Chapter 2.1.1. --- Translation --- p.2-4 / Chapter 2.1.2. --- Rotation --- p.2-5 / Chapter 2.3. --- Orientated Bounding Box (OBB) --- p.2-6 / Chapter 2.4. --- Scan-Line Method --- p.2-7 / Chapter 2.5. --- Mesh Simplification --- p.2-10 / Chapter 2.6. --- Review of the Surface Matching Method --- p.2-12 / Chapter 2.6.1. --- G. Papaioannou et al ´بs method --- p.2-13 / Chapter Chapter 3 --- Genetic Algorithm --- p.3-1 / General introduction --- p.3-1 / Chapter 3.1. --- Characteristics of Genetic Algorithms --- p.3-3 / Chapter 3.2. --- Mechanism of Genetic Algorithms --- p.3-4 / Chapter 3.2.1. --- Coding --- p.3-4 / Chapter 3.2.2. --- Reproduction --- p.3-5 / Chapter 3.2.3. --- Selection --- p.3-8 / Chapter 3.2.4. --- Stopping Criteria --- p.3-9 / Chapter 3.3. --- Convergence of Genetic Algorithms --- p.3-10 / Chapter 3.4. --- Comparison with Traditional Optimization Methods --- p.3-13 / Chapter 3.4.1. --- Test Function - Sphere --- p.3-14 / Chapter 3.4.2. --- Test Function - Rosenbrock's Saddle --- p.3-19 / Chapter 3.4.3. --- Test Function 一 Step --- p.3-22 / Chapter 3.4.4. --- Test Function -Quartic --- p.3-25 / Chapter 3.4.5. --- Test Function - Shekel's Foxholes --- p.3-28 / Chapter 3.5. --- Multi-Objective Genetic Algorithms --- p.3-29 / Chapter 3.5.1. --- Non-Pareto Approach --- p.3-31 / Chapter 3.5.2. --- Pareto-Ranking --- p.3-32 / Chapter 3.5.3. --- Comparison --- p.3-35 / Chapter Chapter 4 --- Assembling broken objects (I) --- p.4-1 / Chapter 4.1. --- System Flow of Single Pair Assemblage --- p.4-2 / Chapter 4.2. --- Parameterization --- p.4-3 / Chapter 4.2.1. --- Degree of Freedom --- p.4-3 / Chapter 4.2.2. --- Reference Plane and Sampling Points --- p.4-4 / Chapter 4.3. --- Matching Error --- p.4-5 / Chapter 4.3.1. --- Counterpart Surface Matching Error --- p.4-5 / Chapter 4.3.2. --- Border Matching Error --- p.4-7 / Chapter 4.4. --- Correlation-Based Matching Method --- p.4-14 / Chapter Chapter 5 --- Assembling Broken Objects (II)- Global Matching --- p.5-1 / Chapter 5.1. --- Arrangement Strategy --- p.5-2 / Chapter 5.1.1. --- Introduction to Packing --- p.5-2 / Chapter 5.1.2. --- Proposed Architecture --- p.5-6 / Chapter 5.2. --- Relational Multi-Objective Genetic Algorithm --- p.5-13 / Chapter 5.2.1. --- Existing Problem --- p.5-13 / Chapter 5.2.2. --- A New Operator --- p.5-14 / Chapter 5.2.3. --- Relationship Function --- p.5-16 / Chapter 5.3. --- Conclusion and summary --- p.5-20 / Chapter Chapter 6 --- Optimization Approach by Genetic Algorithm --- p.6-1 / Chapter 6.1. --- Solution Space --- p.6-1 / Chapter 6.2. --- Formulation of Gene and Chromosome --- p.6-3 / Chapter 6.2.1. --- Matching Three or More Fragments --- p.6-4 / Chapter 6.2.2. --- Matching Two Fragments --- p.6-5 / Chapter 6.3. --- Fitness Function --- p.6-5 / Chapter 6.3.1. --- Matching Two Fragments --- p.6-5 / Chapter 6.3.2. --- Matching Three or More Fragments --- p.6-6 / Chapter 6.4. --- Reproduction --- p.6-7 / Chapter 6.4.1. --- Crossover --- p.6-8 / Chapter 6.4.2. --- Mutation --- p.6-9 / Chapter 6.4.3. --- Inheritance --- p.6-9 / Chapter 6.5. --- Selection --- p.6-9 / Chapter Chapter 7 --- Experimental Results --- p.7-1 / Chapter 7.1 --- Data Acquisition --- p.7-1 / Chapter 7.2 --- Experiment for Mesh Simplification --- p.7-4 / Chapter 7.3 --- Experiment for Correlation-Based Matching Method --- p.7-5 / Chapter 7.4 --- Experiment One: Two Fragments --- p.7-6 / Chapter 7.5 --- Experiment Two: Several Fragments --- p.7-10 / Chapter 7.5.1 --- Constraint Direction Matching --- p.7-10 / Chapter 7.5.2 --- Unconstraint Direction Matching --- p.7-14 / Chapter Chapter 8 --- Conclusion --- p.8-1 / Appendix Reference --- p.1

Lee, Hon Leung. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 98-101) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Preliminaries --- p.11 / Chapter 2.1 --- Functional analysis --- p.11 / Chapter 2.2 --- Convex analysis --- p.14 / Chapter 2.3 --- Relative interiors --- p.19 / Chapter 2.4 --- Multifunctions --- p.21 / Chapter 2.5 --- Variational analysis --- p.22 / Chapter 3 --- A unified notion of optimality --- p.29 / Chapter 3.1 --- Basic notions of minimality --- p.29 / Chapter 3.2 --- A unified notion --- p.32 / Chapter 4 --- Separation theorems --- p.38 / Chapter 4.1 --- Zheng and Ng fuzzy separation theorem --- p.38 / Chapter 4.2 --- Extremal principles and other consequences --- p.43 / Chapter 5 --- Necessary conditions for the unified notion of optimality --- p.49 / Chapter 5.1 --- Local asymptotic closedness --- p.49 / Chapter 5.2 --- First order necessary conditions --- p.56 / Chapter 5.2.1 --- Introductory remark --- p.56 / Chapter 5.2.2 --- Without operator constraints --- p.59 / Chapter 5.2.3 --- With operator constraints --- p.66 / Chapter 5.3 --- Comparisons with known necessary conditions --- p.74 / Chapter 5.3.1 --- Finite-dimensional setting --- p.74 / Chapter 5.3.2 --- Zheng and Ng's work --- p.76 / Chapter 5.3.3 --- Dutta and Tammer's work --- p.80 / Chapter 5.3.4 --- Bao and Mordukhovich's previous work --- p.81 / Chapter 6 --- A weak notion: approximate efficiency --- p.84 / Chapter 6.1 --- Approximate minimality --- p.85 / Chapter 6.2 --- A scalarization result --- p.86 / Chapter 6.3 --- Variational approach --- p.94 / Bibliography --- p.98 / Index --- p.102

Lau Shek Kwan Mark. / "September 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 118-124). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In this thesis we study two important issues in vector optimization problem (VOP). The first is on the scalarization; here we provide some merit functions for VOP and analyze their error bound property. The second is on generalization of Ekeland's variational principle; here this famous result in variational analysis is now extended from the original setting for scalar-valued functions to that of vector-valued functions. This generalization enable us to study the error bound property for systems of functions instead of that for a single function. / Liu Chun-guang. / "June 2006." / Adviser: Kung-fu Ng. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6440. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 92-94). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Fu Peilin. / "February 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 149-157). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Yong Liang. / "November 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 237-266). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

No description available.