Generalized second-order directional derivatives and optimization with C11 functions

Xiaoqi Yang, V. Jeyakumar

Research output: Journal article publicationJournal articleAcademic researchpeer-review

55 Citations (Scopus)


In this paper, a new generalized second-order directional derivative and a set-valued generalized Hessian are introudced for C1,1 functions in real Banach spaces. It is shown that this set-valued generalized Hessian is single-valued at a point if and only if the function is twice weakly Gateaux differentiable at the point and that the generalized second-order directional derivative is upper semi-continuous under a regularity condition. Various generalized calculus rules are also given for C1,1 functions. The generalized second-order directional derivative is applied to derive second-order necessary optimality conditions for mathematical programming problems.
Original languageEnglish
Pages (from-to)165-185
Number of pages21
Issue number3-4
Publication statusPublished - 1 Jan 1992
Externally publishedYes


  • C functions 1,1
  • generalized second-order derivatives
  • nonsmooth analysis
  • second-order necessary conditions

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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