Description: Smooth Nonlinear Optimization in Rn by Tamás Rapcsák 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 Fenchels 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. Fenchels 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) Long Description Experience gained during a ten-year long involvement in modelling, program Review Text ... it is a pleasure to see and read how Tam Review Quote ... it is a pleasure to see and read how Tam Details ISBN0792346807 Short Title SMOOTH NONLINEAR OPTIMIZATION Language English ISBN-10 0792346807 ISBN-13 9780792346807 Media Book Format Hardcover DEWEY 519.76 Series Number 19 Year 1997 Publication Date 1997-08-31 Place of Publication Dordrecht Publisher Springer Birth 1947 Pages 376 Edition 1997th Imprint Springer Country of Publication Netherlands DOI 10.1007/b130874;10.1007/978-1-4615-6357-0 Author Tamás Rapcsák Edition Description 1997 ed. Series Nonconvex Optimization and Its Applications Alternative 9781461379201 Illustrations XIV, 376 p. Audience Undergraduate We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96272268;
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Book Title: Smooth Nonlinear Optimization in Rn
