The upper and lower second order directional derivatives of a sup-type function

Hidefumi Kawasaki

研究成果: Contribution to journalArticle査読

23 被引用数 (Scopus)

抄録

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type function S(x) = sup{f(x, t); t ∈ T} 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, ∂f/∂x and ∂2f/∂x2 are continuous on ℝn× 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.

本文言語英語
ページ(範囲)327-339
ページ数13
ジャーナルMathematical Programming
41
1-3
DOI
出版ステータス出版済み - 5 1 1988

All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 数学 (全般)

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