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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

A survey on numerical methods for unconstrained optimization problems.

January 2002 (has links)
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
22

The strong conical hull intersection property for systems of closed convex sets.

January 2006 (has links)
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
23

On implementation of a self-dual embedding method for convex programming.

January 2003 (has links)
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
24

Assemblage of three-dimensional broken objects using a multi-objective genetic algorithm. / 應用多目標基因演算法於合併三維破裂物件 / Assemblage of three-dimensional broken objects using a multi-objective genetic algorithm. / Ying yong duo mu biao ji yin yan suan fa yu he bing san wei po lie wu jian

January 2004 (has links)
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
25

Recent developments in optimality notions, scalarizations and optimality conditions in vector optimization. / Recent developments in vector optimization

January 2011 (has links)
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
26

Diffusion equation and global optimization. / CUHK electronic theses & dissertations collection

January 2004 (has links)
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.
27

Vector optimization and vector variational principle. / CUHK electronic theses & dissertations collection

January 2006 (has links)
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.
28

Variance minimization and dual control. / CUHK electronic theses & dissertations collection / Digital dissertation consortium

January 2003 (has links)
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.
29

Accelerated strategies of evolutionary algorithms for optimization problem and their applications. / CUHK electronic theses & dissertations collection / Digital dissertation consortium

January 2003 (has links)
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.
30

Optimal quadrature formulae for cetain classes of Hilbert spaces

Elhay, Sylvan. January 1970 (has links) (PDF)
No description available.

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