Some relationships among quasidifferential, weak subdifferential and exhausters

Küçük M., Urbański R., Grzybowski J., Küçük Y., Atasever Güvenç İ., Tozkan D., ...More

Optimization, vol.65, no.11, pp.1949-1961, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 11
  • Publication Date: 2016
  • Doi Number: 10.1080/02331934.2016.1213249
  • Journal Name: Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1949-1961
  • Keywords: Exhauster, quasidifferential, weak subdifferential
  • Uşak University Affiliated: Yes

Abstract

In this study, some relationships between quasidifferentiability and weakly subdifferentiability of a function are investigated, and some results on calculating the quasidifferential in terms of weak exhausters are presented. Moreover, under some assumptions weak subdifferentiability of a quasidifferentiable function is proved and the weak subdifferential is obtained by using the quasidifferential. Under some assumptions, it is proved that a positively homogeneous and lower semicontinuous function is quasidifferentiable. It is also shown that directional differentiability and weak subdifferentiability imply quasidifferentiability. Furthermore, a method to evaluate the quasidifferential is given by using reduced weak lower exhausters.