Titolo: Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (Nonconvex Optimization and Its Applications)
Editore: Springer
Data di pubblicazione: 2014
Lingua: Inglese
ISBN 10: 1461348870
ISBN 13: 9781461348870
Rilegatura: Brossura
Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

Preface. 1. Introduction. 2. Morse theory (without constraints). 3. Morse theory (with constraints). 4. Chebyshev approximation, focal points. 5. Homology, Morse relations. 6. Stability of optimization problems. 7. Transversality. 8. Gradient Flows. 9. Newton flows. 10. Parametric aspects. References. Index. List of symbols.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Descrizione libreria

Hello! Ria Christie Collections is an online venture that was initially set up in 2012 to sell books. We do not have a physical high street store. We are professional online booksellers. We only sell brand new books in perfect condition that we source from various suppliers and the publishers. Primarily, our aim is to provide an excellent service to all our customers. We always work as a team to achieve this. Our other objectives are to: 1. Ensure that all our products reach their destination quickly in a safe and secure manner 2. Answer to all our customer queries within 24 hours 3. Ensure that our customers are happy with their purchases 4. Provide all the items at a competitive price 5. Always listen to our customers Ria Christie Collections is not a registered company. It is a Sole Trader venture. Other key information is shown below: Contact Person Name: Rakesh Luchmun (Mr) Storefront Name: Ria Christie Collections Place of Establishment Address: Suite B; ARUN House; ARUN Building Arundel Road Uxbridge UB8 2RR United Kingdom E-Mail Address: riachristie@hotmail.co.uk VAT Number: GB 160 5650 25 We always work hard and aim to comply with all of Abebooks Policies. If you have any issues, please do not hesitate to write to us whether before or after a purchase. We promise to reply to you promptly and, in any case, within 24 hours. Thank you kindly! Yours sincerely Mr Rakesh Luchmun (Founder) and the Ria Christie Collections Team

Visita la pagina della libreria

Informazioni sull?azienda del venditore

Ryefield Investments Limited
175 Pield Heath Road, Uxbridge, UB8 3NL, United Kingdom

Condizioni di vendita e spedizione

Condizioni di vendita

All Returns and Refund are as per Abebooks policies.

Condizioni di spedizione

Orders usually ship within 2 business days. If your book order is heavy or oversized, we may contact you to let you know extra shipping is required. Thank you!