{"product_id":"nonlinear-optimization-in-finite-dimensions-morse-theory-chebyshev-approximation-transversality-flows-parametric-aspects-9780792365617","title":"Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Hubertus Th Jongen, P. Jonker, F. Twilt\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/31\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 510\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 2.01lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.13d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780792365617\u003cp\u003e\u003ci\u003eThis title is not returnable\u003c\/i\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":40905369190515,"sku":"9.78079E+12","price":372.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_727907e8-b109-4ad5-ab0d-7fbd565b72b3.jpg?v=1690896955","url":"https:\/\/bookstorenmore.com\/en-de\/products\/nonlinear-optimization-in-finite-dimensions-morse-theory-chebyshev-approximation-transversality-flows-parametric-aspects-9780792365617","provider":"Bookstore N More","version":"1.0","type":"link"}