{"product_id":"9781461348870","title":"Nonconvex Optimization and Its Applications: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects","description":"\u003ch1\u003eNonconvex Optimization and Its Applications: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects\u003c\/h1\u003e \u003ch2\u003eJongen, Hubertus Th.; Jonker, P.; Twilt, F.\u003c\/h2\u003e \u003cp\u003eAt 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2014-01-09\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461348870\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4615-0017-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 510\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":45578321166476,"sku":"9781461348870","price":224.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461348870.jpg?v=1775681570","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781461348870","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}