Some relationships among quasidifferential, weak subdifferential and exhausters. (1st November 2016)

• Record Type: Journal Article
• Authors: Küçük, Mahide; Urbański, Ryszard; Grzybowski, Jerzy; Küçük, Yalçın; Atasever Güvenç, İlknur; Tozkan, Didem; Soyertem, Mustafa
• Is Part Of: Optimization. Volume 65:Number 11(2016)
• Page Start: 1949
• Page End: 1961
• Publication Date: 2016-11-01
• Subjects: Exhauster -- quasidifferential -- weak subdifferential; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1213249
• Languages: English
• ISSNs: 0233-1934

Abstract

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.