Some properties of second-order weak subdifferentials

İNCEOĞLU G.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.2, pp.955-960, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2010-22
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.955-960
  • Keywords: Second-order weak subgradient, second-order weak subdifferential, lower semicontinuity, lower Lipschitz function
  • Anadolu University Affiliated: Yes

Abstract

This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-order weakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.