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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 €
+ 763 points
Format
Description
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.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 510
- Langue:
- Anglais
- Collection :
- Tome:
- n° 47
Caractéristiques
- EAN:
- 9781461348870
- Date de parution :
- 09-01-14
- Format:
- Livre broché
- Format numérique:
- Trade paperback (VS)
- Dimensions :
- 156 mm x 234 mm
- Poids :
- 730 g
