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Item Details
| Title:
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NONLINEAR OPTIMIZATION IN FINITE DIMENSIONS
MORSE THEORY, CHEBYSHEV APPROXIMATION, TRANSVERSALITY, FLOWS, PARAMETRIC ASPECTS |
| By: |
Hubertus Th. Jongen, Peter Jonker, Frank Twilt |
| Format: |
Paperback |
| List price:
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£206.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
1461348870 |
| ISBN 13: |
9781461348870 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
9 January, 2014 |
| Edition: |
2000 ed. |
| Series: |
Nonconvex Optimization and Its Applications 47 |
| Pages: |
510 |
| Synopsis: |
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. |
| Illustrations: |
3 Illustrations, black and white; X, 510 p. 3 illus. |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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