Lam Sze Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 93-95). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.4 / Chapter 3 --- Review of Iri-Imai Algorithm for Convex Programming Prob- lems --- p.10 / Chapter 3.1 --- Iri-Imai Algorithm for Convex Programming --- p.11 / Chapter 3.2 --- Numerical Results --- p.14 / Chapter 3.2.1 --- Linear Programming Problems --- p.15 / Chapter 3.2.2 --- Convex Quadratic Programming Problems with Linear Inequality Constraints --- p.17 / Chapter 3.2.3 --- Convex Quadratic Programming Problems with Con- vex Quadratic Inequality Constraints --- p.18 / Chapter 3.2.4 --- Summary of Numerical Results --- p.21 / Chapter 3.3 --- Chapter Summary --- p.22 / Chapter 4 --- Value Estimation Approach to Iri-Imai Method for Con- strained Optimization --- p.23 / Chapter 4.1 --- Value Estimation Function Method --- p.24 / Chapter 4.1.1 --- Formulation and Properties --- p.24 / Chapter 4.1.2 --- Value Estimation Approach to Iri-Imai Method --- p.33 / Chapter 4.2 --- "A New Smooth Multiplicative Barrier Function Φθ+,u" --- p.35 / Chapter 4.2.1 --- Formulation and Properties --- p.35 / Chapter 4.2.2 --- "Value Estimation Approach to Iri-Imai Method by Us- ing Φθ+,u" --- p.41 / Chapter 4.3 --- Convergence Analysis --- p.43 / Chapter 4.4 --- Numerical Results --- p.46 / Chapter 4.4.1 --- Numerical Results Based on Algorithm 4.1 --- p.46 / Chapter 4.4.2 --- Numerical Results Based on Algorithm 4.2 --- p.50 / Chapter 4.4.3 --- Summary of Numerical Results --- p.59 / Chapter 4.5 --- Chapter Summary --- p.60 / Chapter 5 --- Extension of Value Estimation Approach to Iri-Imai Method for More General Constrained Optimization --- p.61 / Chapter 5.1 --- Extension of Iri-Imai Algorithm 3.1 for More General Con- strained Optimization --- p.62 / Chapter 5.1.1 --- Formulation and Properties --- p.62 / Chapter 5.1.2 --- Extension of Iri-Imai Algorithm 3.1 --- p.63 / Chapter 5.2 --- Extension of Value Estimation Approach to Iri-Imai Algo- rithm 4.1 for More General Constrained Optimization --- p.64 / Chapter 5.2.1 --- Formulation and Properties --- p.64 / Chapter 5.2.2 --- Value Estimation Approach to Iri-Imai Method --- p.67 / Chapter 5.3 --- Extension of Value Estimation Approach to Iri-Imai Algo- rithm 4.2 for More General Constrained Optimization --- p.69 / Chapter 5.3.1 --- Formulation and Properties --- p.69 / Chapter 5.3.2 --- Value Estimation Approach to Iri-Imai Method --- p.71 / Chapter 5.4 --- Numerical Results --- p.72 / Chapter 5.4.1 --- Numerical Results Based on Algorithm 5.1 --- p.73 / Chapter 5.4.2 --- Numerical Results Based on Algorithm 5.2 --- p.76 / Chapter 5.4.3 --- Numerical Results Based on Algorithm 5.3 --- p.78 / Chapter 5.4.4 --- Summary of Numerical Results --- p.86 / Chapter 5.5 --- Chapter Summary --- p.87 / Chapter 6 --- Conclusion --- p.88 / Bibliography --- p.93 / Chapter A --- Search Directions --- p.96 / Chapter A.1 --- Newton's Method --- p.97 / Chapter A.1.1 --- Golden Section Method --- p.99 / Chapter A.2 --- Gradients and Hessian Matrices --- p.100 / Chapter A.2.1 --- Gradient of Φθ(x) --- p.100 / Chapter A.2.2 --- Hessian Matrix of Φθ(x) --- p.101 / Chapter A.2.3 --- Gradient of Φθ(x) --- p.101 / Chapter A.2.4 --- Hessian Matrix of φθ (x) --- p.102 / Chapter A.2.5 --- Gradient and Hessian Matrix of Φθ(x) in Terms of ∇xφθ (x) and∇2xxφθ (x) --- p.102 / Chapter A.2.6 --- "Gradient of φθ+,u(x)" --- p.102 / Chapter A.2.7 --- "Hessian Matrix of φθ+,u(x)" --- p.103 / Chapter A.2.8 --- "Gradient and Hessian Matrix of Φθ+,u(x) in Terms of ∇xφθ+,u(x)and ∇2xxφθ+,u(x)" --- p.103 / Chapter A.3 --- Newton's Directions --- p.103 / Chapter A.3.1 --- Newton Direction of Φθ (x) in Terms of ∇xφθ (x) and ∇2xxφθ(x) --- p.104 / Chapter A.3.2 --- "Newton Direction of Φθ+,u(x) in Terms of ∇xφθ+,u(x) and ∇2xxφθ,u(x)" --- p.104 / Chapter A.4 --- Feasible Descent Directions for the Minimization Problems (Pθ) and (Pθ+) --- p.105 / Chapter A.4.1 --- Feasible Descent Direction for the Minimization Prob- lems (Pθ) --- p.105 / Chapter A.4.2 --- Feasible Descent Direction for the Minimization Prob- lems (Pθ+) --- p.107 / Chapter B --- Randomly Generated Test Problems for Positive Definite Quadratic Programming --- p.109 / Chapter B.l --- Convex Quadratic Programming Problems with Linear Con- straints --- p.110 / Chapter B.l.1 --- General Description of Test Problems --- p.110 / Chapter B.l.2 --- The Objective Function --- p.112 / Chapter B.l.3 --- The Linear Constraints --- p.113 / Chapter B.2 --- Convex Quadratic Programming Problems with Quadratic In- equality Constraints --- p.116 / Chapter B.2.1 --- The Quadratic Constraints --- p.117
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324006 |
| Date | January 2002 |
| Contributors | Lam, Sze Wan., Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ix, 120 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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