| 書目名稱 | Nonlinear Optimization in Finite Dimensions | | 副標題 | Morse Theory, Chebys | | 編輯 | Hubertus Th. Jongen,Peter Jonker,Frank Twilt | | 視頻video | http://file.papertrans.cn/668/667609/667609.mp4 | | 叢書名稱 | Nonconvex Optimization and Its Applications | | 圖書封面 |  | | 描述 | 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 a | | 出版日期 | Book 2000 | | 關(guān)鍵詞 | Approximation; global optimization; homology; linear optimization; nonlinear optimization; operations res | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4615-0017-9 | | isbn_softcover | 978-1-4613-4887-0 | | isbn_ebook | 978-1-4615-0017-9Series ISSN 1571-568X | | issn_series | 1571-568X | | copyright | Springer Science+Business Media Dordrecht 2000 |
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