Some relationships among quasidifferential, weak subdifferential and exhausters

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

Optimization, cilt.65, sa.11, ss.1949-1961, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 11
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/02331934.2016.1213249
  • Dergi Adı: Optimization
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1949-1961
  • Anahtar Kelimeler: Exhauster, quasidifferential, weak subdifferential
  • Uşak Üniversitesi Adresli: Evet

Özet

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.