UPPER AND LOWER SECOND ORDER DIRECTIONAL DERIVATIVES OF A SUP-TYPE FUNCTION.

Hidefumi Kawasaki

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The purpose of this paper is to give a formula for expessing the second order directional derivatives of the sup-type function S(x) equals sup left brace f(x,t); epsilon TRTBC in terms of the first and second derivatives of f(x,t), where T is a compact set in a metric space and we assume that f, PARTIAL T right brace in terms of the first and second drivatives of f(x,t), where T is a compact set in a metric space and we assume that f, PARTIAL f/ PARTIAL x and PARTIAL **2**4f/ PARTIAL x**2 are continuous on R double prime multiplied by T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition for S(x) to be directionally twice differentiable.

    Original languageEnglish
    Pages (from-to)327-339
    Number of pages13
    JournalMathematical Programming
    Volume41
    Issue number3
    Publication statusPublished - Sept 1988

    All Science Journal Classification (ASJC) codes

    • Computer Graphics and Computer-Aided Design
    • Software
    • Management Science and Operations Research
    • Safety, Risk, Reliability and Quality
    • General Mathematics
    • Applied Mathematics

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