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Nonlinear Optimization in Finite Dimensions
Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects
Hubertus Th Jongen, P Jonker, F Twilt
€ 381,95
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Omschrijving
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.
Specificaties
Betrokkenen
- Auteur(s):
- Uitgeverij:
Inhoud
- Aantal bladzijden:
- 510
- Taal:
- Engels
- Reeks:
- Reeksnummer:
- nr. 47
Eigenschappen
- Productcode (EAN):
- 9781461348870
- Verschijningsdatum:
- 9/01/2014
- Uitvoering:
- Paperback
- Formaat:
- Trade paperback (VS)
- Afmetingen:
- 156 mm x 234 mm
- Gewicht:
- 730 g
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