Name: Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (en Inglés)
SKU: 58147973
Price: 219.93 USD
Availability: InStock
Author: Jongen, Hubertus Th ; Jonker, P. ; Twilt, F.
ISBN: 9781461348870

portada Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (en Inglés)

Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (en Inglés)

Formato

Libro Físico

Autor

Editorial

Idioma

Inglés

N° páginas

510

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x2.7 cm

Peso

0.73 kg.

ISBN13

9781461348870

Categorías

Cálculo y análisis matemático
Teoría del juego
Matemáticas aplicadas

Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (en Inglés)

Hubertus Th Jongen (Autor) · P. Jonker (Autor) · F. Twilt (Autor) · Springer · Tapa Blanda

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Reseña del libro "Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (en Inglés)"

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.