Some relationships among gw-subdifferential, directional derivative and radial epiderivative for nonconvex vector functions

KÜÇÜK Y., Atasever İ., KÜÇÜK M.

Optimization, vol.64, no.3, pp.627-640, 2015 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 64 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1080/02331934.2013.793328
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.627-640
  • Keywords: 65K10, 28B99, 49J52, 26A24, non-convex optimization, directional derivative, radial epiderivative, contingent epiderivative, contingent derivative, generalized weak subdifferential, SET-VALUED OPTIMIZATION, OPTIMALITY CONDITIONS
  • Anadolu University Affiliated: Yes

Abstract

© 2013, Taylor & Francis.In this work, we give some characterizations of gw-subdifferentiability of a vector-valued function by using its directional derivative and radial epiderivative. Moreover, under some assumptions, we proved that the directional derivative and radial epiderivative of a vector-valued function are the elements of the supremum set of gw-subgradients of it. Finally, without any convexity assumption, we proved that the epigraph of contingent derivative of a set valued map is included in the epigraph of contingent epiderivative of this set-valued map.