Thạc Sĩ Coderivatives of normal cone mappings and applications

Contents
Table of Notations vi
List of Figures viii
Introduction ix
Chapter 1. Preliminary 1
1.1 Basic Definitions and Conventions 1
1.2 Normal and Tangent Cones . 3
1.3 Coderivatives and Subdifferential 6
1.4 Lipschitzian Properties and Metric Regularity . 9
1.5 Conclusions 11
Chapter 2. Linear Perturbations of Polyhedral Normal Cone
Mappings 12
2.1 The Normal Cone Mapping F(x, b) . 12
2.2 The Fr´echet Coderivative of F(x, b) . 16
2.3 The Mordukhovich Coderivative of F(x, b) . 26
2.4 AVIs under Linear Perturbations 37
2.5 Conclusions 42
Chapter 3. Nonlinear Perturbations of Polyhedral Normal Cone
Mappings 43
3.1 The Normal Cone Mapping F(x, A, b) 43
3.2 Estimation of the Fr´echet Normal Cone to gphF 48
3.3 Estimation of the Limiting Normal Cone to gphF . 54
iv3.4 AVIs under Nonlinear Perturbations . 59
3.5 Conclusions 66
Chapter 4. A Class of Linear Generalized Equations 67
4.1 Linear Generalized Equations 67
4.2 Formulas for Coderivatives 69
4.2.1 The Fr´echet Coderivative of N (x, α) 70
4.2.2 The Mordukhovich Coderivative of N (x, α) 78
4.3 Necessary and Sufficient Conditions for Stability 83
4.3.1 Coderivatives of the KKT point set map 83
4.3.2 The Lipschitz-like property 84
4.4 Conclusions 91
General Conclusions 92
List of Author’s Related Papers 93
Refer