Relationships Between Convexificators and Greenberg–Pierskalla Subdifferentials for Quasiconvex Functions. (2nd December 2017)

• Record Type: Journal Article
• Authors: Kabgani, Alireza; Soleimani-damaneh, Majid
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 12(2017)
• Page Start: 1548
• Page End: 1563
• Publication Date: 2017-12-02
• Subjects: Convexificator -- Greenberg–Pierskalla subdifferentials -- nonsmooth analysis -- quasiconvexity; 49J52 -- 26A51; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1349144
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, the relationship between convexificators and Greenberg–Pierskalla-based (GP-based) subdifferentials for quasiconvex functions is proved. The established results lead to a mean value theorem, a chain rule, and the closedness property for GP-based subdifferentials. Furthermore, the connection between Clarke generalized gradient and Mordukhovich subdifferential with GP-based subdifferentials is highlighted.