Relationships Between Convexificators and Greenberg–Pierskalla Subdifferentials for Quasiconvex Functions
Alireza Kabgani, Majid Soleimani-damaneh · Numerical Functional Analysis and Optimization · 2017
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.