On Optimization via -Generalized Weak Subdifferentials

P. Cheraghi, A.P. Farajzadeh, S. Suantai

Abstract

In this paper, we study -generalized weak subdifferential for functions defined on a real topological vector space. Some necessary and sufficient conditions for having nonempty -generalized weak subdifferential of a function are presented. The positively homogenous of the -generalized weak subdifferential operator is proved. A necessary and sufficient conditions for achieving a global minimum of a -generalized weak subdifferentiable function is stated. A link between sudifferential and Fr´echet differential with -generalized weak subdifferential is established. Finally a result about the equality of the fuzzy sum rule inclusion is investigated.