{"product_id":"nonlinear-optimization-in-finite-dimensions-hubertus-th-jongen-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\u003eISBN-10:\u003c\/b\u003e 0792365615\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792365617\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/31\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 510\u003cbr\u003e\u003cb\u003eFormat:\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","brand":"Hubertus Th Jongen","offers":[{"title":"Hardcover","offer_id":44120214962431,"sku":"9780792365617","price":249.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_63f4e98c-2b36-4b3a-8996-439ccc820f2e.jpg?v=1687413131","url":"https:\/\/www.whiterainbookhouse.com\/products\/nonlinear-optimization-in-finite-dimensions-hubertus-th-jongen-9780792365617","provider":"WR Book House","version":"1.0","type":"link"}