One-parameter families of optimization problems: equality constraints

H.Th. Jongen, P. Jonker, F. Twilt

    Research output: Contribution to journalArticleAcademic

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    Abstract

    In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.
    Original languageUndefined
    Pages (from-to)141-161
    JournalJournal of optimization theory and applications
    Volume48
    Issue number1
    DOIs
    Publication statusPublished - 1988

    Keywords

    • critical points
    • Parametric Optimization
    • Quadratic Index
    • Linear Index
    • Morse index
    • (generalized) critical points
    • IR-85873

    Cite this

    Jongen, H.Th. ; Jonker, P. ; Twilt, F. / One-parameter families of optimization problems: equality constraints. In: Journal of optimization theory and applications. 1988 ; Vol. 48, No. 1. pp. 141-161.
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    author = "H.Th. Jongen and P. Jonker and F. Twilt",
    year = "1988",
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    One-parameter families of optimization problems: equality constraints. / Jongen, H.Th.; Jonker, P.; Twilt, F.

    In: Journal of optimization theory and applications, Vol. 48, No. 1, 1988, p. 141-161.

    Research output: Contribution to journalArticleAcademic

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    AU - Jonker, P.

    AU - Twilt, F.

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    AB - In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.

    KW - critical points

    KW - Parametric Optimization

    KW - Quadratic Index

    KW - Linear Index

    KW - Morse index

    KW - (generalized) critical points

    KW - IR-85873

    U2 - 10.1007/BF00938594

    DO - 10.1007/BF00938594

    M3 - Article

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