Generalized hessian for C1,1 functions in infinite dimensional normed spaces

Z. Páles, Vera Zeidan

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The subject of this paper is the systematic study of second order notions concerning differentiable functions with Lipschitz derivative. The results and notions are motivated by recent papers of Cominetti, Correa and Hiriart-Urruty. The first goal of this paper is the comparison of several known second order directional derivatives. The second goal is the introduction of a generalized Hessian which is a set of certain symmetric bilinear forms. The relation of this generalized Hessian to other existing second order derivatives is also described.

Original languageEnglish
Pages (from-to)59-78
Number of pages20
JournalMathematical Programming, Series B
Volume74
Issue number1
DOIs
Publication statusPublished - Jul 1996

Fingerprint

Second-order Derivatives
Infinite-dimensional Spaces
Normed Space
Derivatives
Directional derivative
Bilinear form
Differentiable
Lipschitz
Derivative

Keywords

  • C functions
  • Generalized directional derivatives
  • Generalized Hessian
  • Infinite dimensional normed space

ASJC Scopus subject areas

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

Cite this

Generalized hessian for C1,1 functions in infinite dimensional normed spaces. / Páles, Z.; Zeidan, Vera.

In: Mathematical Programming, Series B, Vol. 74, No. 1, 07.1996, p. 59-78.

Research output: Contribution to journalArticle

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