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Nonconvex Optimization and Its Applications

Nonlinear Optimization in Finite Dimensions

Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects

Authors: Jongen, Hubertus Th., Jonker, P., Twilt, F.

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  • ISBN 978-1-4615-0017-9
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Hardcover 207,99 €
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Softcover 207,99 €
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  • ISBN 978-1-4613-4887-0
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About this book

At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn­ Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil­ ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under­ standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol­ ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 166,59 €
price for Spain (gross)
  • ISBN 978-1-4615-0017-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 207,99 €
price for Spain (gross)
  • ISBN 978-0-7923-6561-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 207,99 €
price for Spain (gross)
  • ISBN 978-1-4613-4887-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Optimization in Finite Dimensions
Book Subtitle
Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects
Authors
Series Title
Nonconvex Optimization and Its Applications
Series Volume
47
Copyright
2000
Publisher
Springer US
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4615-0017-9
DOI
10.1007/978-1-4615-0017-9
Hardcover ISBN
978-0-7923-6561-7
Softcover ISBN
978-1-4613-4887-0
Series ISSN
1571-568X
Edition Number
1
Number of Pages
X, 510
Number of Illustrations
3 b/w illustrations
Topics