| 书目名称 | Nonlinear Optimization in Finite Dimensions | | 副标题 | Morse Theory, Chebys | | 编辑 | Hubertus Th. Jongen,Peter Jonker,Frank Twilt | | 视频video | | | 丛书名称 | Nonconvex Optimization and Its Applications | | 图书封面 |  | | 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 | | 关键词 | 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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发表于 2025-3-21 18:19:58
