Smooth Nonlinear Optimization in Rn

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Tamás Rapcsák

   Pages 1-6

3. Nonlinear Optimization Problems

   • Tamás Rapcsák

   Pages 7-25

4. Optimality Conditions

   • Tamás Rapcsák

   Pages 27-36

5. Geometric Background of Optimality Conditions

   • Tamás Rapcsák

   Pages 37-44

6. Deduction of the Classical Optimality Conditions in Nonlinear Optimization

   • Tamás Rapcsák

   Pages 45-60

7. Geodesic Convex Functions

   • Tamás Rapcsák

   Pages 61-86

8. On the Connectedness of the Solution Set to Complementarity Systems

   • Tamás Rapcsák

   Pages 87-110

9. Nonlinear Coordinate Representations

   • Tamás Rapcsák

   Pages 111-139

10. Tensors in Optimization

    • Tamás Rapcsák

    Pages 141-166

11. Geodesic Convexity on R ⁿ₊

    • Tamás Rapcsák

    Pages 167-183

12. Variable Metric Methods Along Geodesics

    • Tamás Rapcsák

    Pages 185-206

13. Polynomial Variable Metric Methods For Linear Optimization

    • Tamás Rapcsák

    Pages 207-230

14. Special Function Classes

    • Tamás Rapcsák

    Pages 231-251

15. Fenchel’s Unsolved Problem of Level Sets

    • Tamás Rapcsák

    Pages 253-270

16. An Improvement of the Lagrange Multiplier Rule for Smooth Optimization Problems

    • Tamás Rapcsák

    Pages 271-284

17. Back Matter

    Pages 285-375

    PDF

Experience gained during a ten-year long involvement in modelling, program­ ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in­ dispensable. This is the reason why I have chosen the field in question as the sphere of my research. Since in applications, mainly from among the nonconvex optimization models, the differentiable ones proved to be the most efficient in modelling, especially in solving them with computers, I started to deal with the structure of smooth optimization problems. The book, which is a result of more than a decade of research, can be equally useful for researchers and stu­ dents showing interest in the domain, since the elementary notions necessary for understanding the book constitute a part of the university curriculum. I in­ tended dealing with the key questions of optimization theory, which endeavour, obviously, cannot bear all the marks of completeness. What I consider the most crucial point is the uniform, differential geometric treatment of various questions, which provides the reader with opportunities for learning the structure in the wide range, within optimization problems. I am grateful to my family for affording me tranquil, productive circumstances. I express my gratitude to F.

• Optimality Conditions
• Optimization algorithm
• Optimization algorithms
• algorithms
• linear optimization
• nonlinear optimization
• optimization
• sets

`... it is a pleasure to see and read how Tamás Rapcsák combines differential geometry and other high-level mathematics to model and solve problems which belong to smooth nonlinear optimization. The book can be highly recommended to researchers and graduate students interested in optimization theory. In summary, this book is a vaulable contribution to the existing literature on smooth optimization in finite dimension.'
Optimization, 46 (1999)

• Computer and Automation Institute of Hungarian Academy of Sciences, Budapest, Hungary

  Tamás Rapcsák

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