Smooth Nonlinear Optimization in Rn

AvTamás Rapcsák

Inbunden, Engelska, 1997

Del 19 i serien Nonconvex Optimization and Its Applications

2 110 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

2 320 kr

Skickas inom 10-15 vardagar

Beskrivning

This is a differential geometric approach to smooth nonlinear optimization. This allows the author to improve the sufficiency part of the Lagrange multiplier rule introduced in 1788 and to solve Fenchel's problem of level sets (1953) in the smooth case. Furthermore, this permits the author to replace convexity by geodesic convexity and apply it in complementarity systems, to study the nonlinear coordinate representations of smooth optimization problems, to describe the structure by tensors, to introduce a general framework for variable metric methods containing many basic nonlinear optimization algorithms and, last but not least, to generate a class of polynomial interior point algorithms for linear optimization by a subclass of Riemannian metrics.

Produktinformation

Utgivningsdatum:1997-08-31
Mått:156 x 234 x 26 mm
Vikt:758 g
Format:Inbunden
Språk:Engelska
Serie:Nonconvex Optimization and Its Applications
Antal sidor:376
Upplaga:1997
Förlag:Kluwer Academic Publishers
ISBN:9780792346807

Utforska kategorier

Recensioner i media

'... it is a pleasure to see and read how Tamas Rapcsak 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)

Innehållsförteckning

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.