An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems

Hidefumi Kawasaki

    Research output: Contribution to journalArticlepeer-review

    112 Citations (Scopus)

    Abstract

    A group of curves generates a new curve which is called an envelope. When one deals with a minimization problem with infinitely many inequality constraints, one must encounter an envelopelike effect caused by the constraints. In this paper we present second-order necessary conditions, which involve a new term besides the second derivative of the Lagrange function. We apply our results to minimizing problems of sup-type functions. One will observe in examples that the new term given in this paper explains well the behavior of the second directional derivative of the sup-type function.

    Original languageEnglish
    Pages (from-to)73-96
    Number of pages24
    JournalMathematical Programming
    Volume41
    Issue number1-3
    DOIs
    Publication statusPublished - May 1988

    All Science Journal Classification (ASJC) codes

    • Software
    • General Mathematics

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