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    Nonlinear Optimization in Finite Dimensions: Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects (Nonconvex Optimization and Its Applications) (Hardback) By (author) Hubertus Th. Jongen, By (author) Peter Jonker, By (author) Frank Twilt

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    DescriptionAt 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.


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    Title
    Nonlinear Optimization in Finite Dimensions
    Subtitle
    Morse Theory, Chebyshev Approximation, Transversality, Flows, Parametric Aspects
    Authors and contributors
    By (author) Hubertus Th. Jongen, By (author) Peter Jonker, By (author) Frank Twilt
    Physical properties
    Format: Hardback
    Number of pages: 520
    Width: 155 mm
    Height: 235 mm
    Thickness: 28 mm
    Weight: 2,010 g
    Language
    English
    ISBN
    ISBN 13: 9780792365617
    ISBN 10: 0792365615
    Classifications

    BIC E4L: COM
    Nielsen BookScan Product Class 3: S10.2
    B&T Book Type: NF
    LC subject heading:
    B&T Merchandise Category: TXT
    BIC subject category V2: PBW
    B&T General Subject: 710
    B&T Modifier: Continuations: 02
    B&T Modifier: Region of Publication: 04
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    Libri: I-MA
    LC subject heading: ,
    BISAC V2.8: MAT017000
    LC subject heading:
    Warengruppen-Systematik des deutschen Buchhandels: 16290
    BISAC V2.8: MAT011000
    B&T Approval Code: A51862000
    DC21: 519.3
    LC subject heading:
    BISAC V2.8: MAT037000
    BIC subject category V2: PBU
    DC22: 519.3
    B&T Approval Code: A51440000
    LC classification: QA402.3, QA372
    BIC subject category V2: UMG
    LC classification: QA402.5 .J57 2000
    LC subject heading:
    LC classification: QA1-939, QA315-316, QA402.5-402.6, QA612-612.8, QA614-614.97
    LC subject heading:
    Thema V1.0: PBW, PBU, UMG
    Edition statement
    2001 ed.
    Illustrations note
    3 black & white illustrations, biography
    Publisher
    Kluwer Academic Publishers
    Imprint name
    Kluwer Academic Publishers
    Publication date
    31 October 2000
    Publication City/Country
    Dordrecht, Netherlands
    Table of contents
    Preface. 1. Introduction. 2. Morse theory (without constraints). 3. Morse theory (with constraints). 4. Chebyshev approximation, focal points. 5. Homology, Morse relations. 6. Stability of optimization problems. 7. Transversality. 8. Gradient Flows. 9. Newton flows. 10. Parametric aspects. References. Index. List of symbols.