A generalized upper Dini-directional derivative in vector optimization

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3 Citations (Scopus)

Abstract

In this paper, a set-valued generalized upper Dini-directional derivative is introduced for a locally Lipschitz vector-valued function. Some properties, such as sum formula and chain rule, of this upper Dini-directional derivative are derived. This upper Dini-directional derivative is applied to characterize a cone-convex function and a vector subdifferential and to derive optimality conditions for a multi-objective optimization problem with a locally Lipschitz vector-valued objective function over a convex set. Published under license under the Gordon and Breach Science Publishers imprint.
Original languageEnglish
Pages (from-to)339-351
Number of pages13
JournalOptimization
Volume43
Issue number4
DOIs
Publication statusPublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Lipschitz vector-valued function
  • Optimality condition
  • Upper Dini-directional derivative
  • Weak subdifferential

ASJC Scopus subject areas

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

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