On generalized weak subdifferentials and some properties

KÜÇÜK Y., ATASEVER GÜVENÇ İ., Kucuk M.

OPTIMIZATION, vol.61, no.12, pp.1369-1381, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 12
  • Publication Date: 2012
  • Doi Number: 10.1080/02331934.2011.564622
  • Journal Name: OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1369-1381
  • Keywords: nonconvex analysis, nonsmooth analysis, generalized weak subdifferentials, generalized lower Lipschitz functions, nonconvex optimization, RADIAL EPIDERIVATIVES
  • Anadolu University Affiliated: Yes

Abstract

In this article, some characterizations for gw-subdifferentiability of functions from R-n to R-m are stated. Some criteria for gw-subdifferentiability of generalized lower locally Lipschitz functions and positively homogeneous functions are given. Furthermore, it is proved that every Lipschitz function is gw-subdifferentiable at any point in its domain. Finally, the relationship between directional derivative and gw-subdifferential is given and a convexity criteria for Frechet differentiable function is given by using gw-subdifferential.