Smooth Nonlinear Optimization in Rn (Hardcover)

Tamas Rapcsak

ISBN 10: 0792346807 / ISBN 13: 9780792346807

Editore: Kluwer Academic Publishers, Dordrecht, 1997

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Hardcover. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780792346807

Dati bibliografici

• Titolo: Smooth Nonlinear Optimization in Rn (Hardcover)
• Editore: Kluwer Academic Publishers, Dordrecht
• Data di pubblicazione: 1997
• Lingua: Inglese
• ISBN 10: 0792346807
• ISBN 13: 9780792346807
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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.

Recensione

`... 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)