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

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Abstract

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.

Original languageEnglish
Pages (from-to)327-339
Number of pages13
JournalMathematical Programming
Volume41
Issue number1-3
DOIs
Publication statusPublished - May 1 1988

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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