Introduction to the Theory of Nonlinear Optimization (eBook)

Johannes Jahn (Autor)

eBook Download: PDF

2007 | 3., Third Edition 2007
X, 292 Seiten
Springer Berlin (Verlag)
978-3-540-49379-2 (ISBN)

Infos

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Inhalt

Preface 6
Contents 7
Chapter 1 Introduction and Problem Formulation 9
Chapter 2 Existence Theorems for Minimal Points 14
2.1 Problem Formulation 14
2.2 Existence Theorems 15
2.3 Set of Minimal Points 25
2.4 Application to Approximation Problems 26
2.5 Application to Optimal Control Problems 30
Exercises 36
Chapter 3 Generalized Derivatives 38
3.1 Directional Derivative 38
3.2 Gateaux and Prechet Derivatives 44
3.3 Subdifferential 56
3.4 Quasidifferential 64
3.5 Clarke Derivative 74
Exercises 82
Chapter 4 Tangent Cones 85
4.1 Definition and Properties 85
4.2 Optimality Conditions 94
4.3 A Lyusternik Theorem 101
Exercises 109
Chapter 5 Generalized Lagrange Multiplier Rule 111
5.1 Problem Formulation 111
5.2 Necessary Optimality Conditions 114
5.3 Sufficient Optimality Conditions 132
5.4 Application to Optimal Control Problems 142
Exercises 162
Chapter 6 Duality 165
6.1 Problem Formulation 165
6.2 Duality Theorems 170
6.3 Saddle Point Theorems 174
6.4 Linear Problems 178
6.5 Application to Approximation Problems 181
Exercises 190
Chapter 7 Application to Extended Semidefinite Optimization 192
7.1 Lowner Ordering Cone and Exten-sions 192
7.2 Optimality Conditions 207
7.3 Duality 212
Exercises 215
Chapter 8 Direct Treatment of Special Optimization Problems 217
8.1 Linear Quadratic Optimal Control Problems 217
8.2 Time Minimal Control Problems 225
Exercises 242
Appendix A Weak Convergence 245
Appendix B Reflexivity of Banach Spaces 247
Appendix C Hahn- Banach Theorem 249
Appendix D Partially Ordered Linear Spaces 253
Bibliography 256
Answers to the Exercises 278
Index 292

Produkt-Details

• Erscheint lt. Verlag: 30.6.2007
• Zusatzinfo: X, 292 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation
• Schlagworte: Calculus of Variations • Control Theory • linear optimization • Nonlinear Optimization • Optimality conditions • Optimization • optimization theory • Vector Optimization
• ISBN-10: 3-540-49379-4 / 3540493794
• ISBN-13: 978-3-540-49379-2 / 9783540493792