On Optimization via $\epsilon$-Generalized Weak Subdifferentials
P. Cheraghi, Ali P. Farajzadeh, Suthep Suantai · Thai Journal of Mathematics · 2018
In this paper, we study $\epsilon$-generalized subdifferential for functions defined on a real topologicalvector space. Some necessary and sufficient conditions for having nonempty $\epsilon$- generalizedsubdifferential of a function are presented. The positively homogenous of the $\epsilon$- generalizedsubdifferential operator is proved. A necessary and sufficient conditions for achieving a globalminimum of a $\epsilon$- generalized subdifferential function is stated. A link between sudifferentialand Frechet differential with $\epsilon$- generalized subdifferential is established. Finally a result aboutthe equality of the fuzzy sum rule inclusion is investigated.