Smooth Nonlinear Optimization in Rn
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Smooth Nonlinear Optimization in Rn: (19 Nonconvex Optimization and Its Applications)

Smooth Nonlinear Optimization in Rn: (19 Nonconvex Optimization and Its Applications)


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About the Book

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.

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.

Review :
`... 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)


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Product Details
  • ISBN-13: 9780792346807
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 234 mm
  • No of Pages: 376
  • Returnable: Y
  • Width: 156 mm
  • ISBN-10: 0792346807
  • Publisher Date: 31 Aug 1997
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 19 Nonconvex Optimization and Its Applications


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Smooth Nonlinear Optimization in Rn: (19 Nonconvex Optimization and Its Applications)
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