Smooth Nonlinear Optimization in Rn / Edition 1

by Tamás Rapcsák

Overview

Experience gained during a ten-year long involvement in modelling, programming 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 students 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.

Product Details

ISBN-13:	9780792346807
Publisher:	Springer US
Publication date:	08/31/1997
Series:	Nonconvex Optimization and Its Applications , #19
Edition description:	1997
Pages:	376
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

Preface. 1. Introduction. 2. Nonlinear Optimization Problems. 3. Optimality Conditions. 4. Geometric Background of Optimality Conditions. 5. Deduction of the Classical Optimality Conditions in Nonlinear Optimization. 6. Geodesic Convex Functions. 7. On the Connectedness of the Solution Set to Complementarity Systems. 8. Nonlinear Coordinate Representations. 9. Tensors in Optimization. 10. Geodesic Convexity on R°n+ 11. Variable Metric Methods Along Geodesics. 12. Polynomial Variable Metric Methods for Linear Optimization. 13. Special Function Classes. 14. Fenchel's Unsolved Problem of Level Sets. 15. An Improvement of the Lagrange Multiplier Rule for Smooth Optimization Problems. A. On the Connection Between Mechanical Force Equilibrium and Nonlinear Optimization. B. Topology. C. Riemannian Geometry. References. Author Index. Subject Index. Notations.

Editorial Reviews

‘... 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)

From the Publisher

Designed for researchers and graduate students, addresses key questions of optimization theory and demonstrates that the tools of differential geometry can be used with success in the case of smooth problems, especially convex problems arising in nonlinear optimization. Rapcs<'a>k (computer and automation studies, Hungarian Academy of Sciences) solves Fenchel's problem of level sets in the smooth case; replaces convexity with geodesic convexity; and studies the nonlinear coordinate representations of smooth optimization problems. Annotation c. by Book News, Inc., Portland, Or.

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