An Algorithmic Approach to Nonlinear Analysis and Optimization

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Front Cover 2
An Algorithmic Approach to Nonlinear Analysis and Optimization 5
Copyright Page 6
Preface 9
Acknowledgments 13
CONTENTS 15
Chapter 1. Iterative Methods on Normed Linear Spaces 19
- 1.1 Introduction 19
- 1.2 Contraction Mappings 22
- 1.3 Differentiation on Normed Spaces 33
- 1.4 Gradient Techniques 45
- 1.5 Least Squares Approximation 63
- 1.6 Two-Point Boundary Value Problems 72
- 1.7 Further Remarks on Stability 80
Chapter 2. Constrained Optimization on En 85

Front Cover 2
An Algorithmic Approach to Nonlinear Analysis and Optimization 5
Copyright Page 6
Preface 9
Acknowledgments 13
CONTENTS 15
Chapter 1. Iterative Methods on Normed Linear Spaces 19
- 1.1 Introduction 19
- 1.2 Contraction Mappings 22
- 1.3 Differentiation on Normed Spaces 33
- 1.4 Gradient Techniques 45
- 1.5 Least Squares Approximation 63
- 1.6 Two-Point Boundary Value Problems 72
- 1.7 Further Remarks on Stability 80
Chapter 2. Constrained Optimization on En 85
- 2.1 Introduction 85
- 2.2 Semicontinuity and Convexity 86
- 2.3 A Penalty Argument 96
- 2.4 The Kuhn–Tucker and Lagrange Multiplier Rules 105
- 2.5 The Regularity Assumption 116
- 2.6 Bibliographic Notes and Other Remarks 123
Chapter 3. Computational Techniques for Constrained Optimization on En 128
- 3.1 Introduction 128
- 3.2 Implementation of the Penalty Argument 129
- 3.3 A Conjugate Direction Method 138
- 3.4 Gradient Projection 150
- 3.5 Numerical Examples and One-Dimensional Minimization 163
- 3.6 Bibliographic Notes and Remarks 169
Chapter 4. Constrained Optimization in Function Space 177
- 4.1 Introduction 177
- 4.2 Problems of Optimal Control 178
- 4.3 The Neyman–Pearson Multiplier Rule 189
Chapter 5. Weak Convergence in Hilbert Space 203
- 5.1 Introduction 203
- 5.2 Weak Convergence 204
- 5.3 Fixed Points of Nonexpansive Maps 211
- 5.4 The Penalty Argument in Hilbert Space 217
- 5.5 An Existence Question in Optimization 219
Appendix: Computer Program for the Solution of Two-Point Boundary Value Problems 222
Bibliography 247
AUTHOR INDEX 249
SUBJECT INDEX 251
Mathematics in Science and Engineering 254

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