Nonlinear Optimization in Finite Dimensions

Name: Nonlinear Optimization in Finite Dimensions
Brand: Springer, Berlin
SKU: 9780792365617
Price: 1061.95 PLN
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Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects

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

Język:

Oprawa: Twarda

Wydawca: Springer, Berlin

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At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of...

Informacje o książce

Autor

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

Język

Angielski

Oprawa

Książka - Twarda

Data wydania

2000

strony

510

EAN

9780792365617

ISBN

0792365615

Enbook ID

02705417

Wydawca

Springer, Berlin

Waga

932

Wymiary

160 x 240 x 28

Pełny opis

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.

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Nonlinear Optimization in Finite Dimensions

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

Informacje o książce

Pełny opis

Możesz być zainteresowany

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