### 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 language | English |
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Pages (from-to) | 327-339 |

Number of pages | 13 |

Journal | Mathematical Programming |

Volume | 41 |

Issue number | 3 |

Publication status | Published - Sep 1988 |

### All Science Journal Classification (ASJC) codes

- Computer Graphics and Computer-Aided Design
- Software
- Management Science and Operations Research
- Safety, Risk, Reliability and Quality
- Mathematics(all)
- Applied Mathematics