On relations and applications of generalized second-order directional derivatives

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20 Citations (Scopus)

Abstract

Relations among upper and lower generalized second-order directional derivatives for a locally Lipschitz function are derived. In addition, existence conditions are determined for second-order directional derivatives. The resulting relations and conditions are used to characterize the convexity property of a locally Lipschitz function and to compare generalized Hessians and second-order optimality conditions. Finally, it is demonstrated that a Cominetti-Correa-type directional derivative is bounded below by the conjugacy of a Ben-Tal-Zowe-type directional derivative.
Original languageEnglish
Pages (from-to)595-614
Number of pages20
JournalNonlinear Analysis, Theory, Methods and Applications
Volume36
Issue number5
DOIs
Publication statusPublished - 1 Jun 1999
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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