%0 Journal Article %T Some relations between ε-directional derivative and ε-generalized weak subdifferential %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Mohebi, A. %A Mohebi, H. %D 2015 %\ 09/01/2015 %V 2 %N 1 %P 65-80 %! Some relations between ε-directional derivative and ε-generalized weak subdifferential %K Non-convex optimization %K "-directional derivative %R %X In this paper, we study ε-generalized weak subdifferential for vector valued functions defined on a real ordered topological vector space X. We give various characterizations of ε-generalized weak subdifferential for this class of functions. It is well known that if the function f : X → R is subdifferentiable at x0 ∈ X, then f has a global minimizer at x0 if and only if 0 ∈ ∂ f(x0). We show that a similar result can be obtained for ε-generalized weak subdifferential. Finally, we investigate some relations between ε-directional derivative and ε-generalized weak subdifferential. In fact, in the classical subdifferential theory, it is well known that if the function f : X → R is subdifferentiable at x0 ∈ X and it has directional derivative at x0 in the direction u ∈ X, then the relation f ′(x0, u) ≥ ⟨u, x∗⟩, ∀ x∗ ∈ ∂ f(x0) is satisfied. We prove that a similar result can be obtained for ε- generalized weak subdifferential. %U https://wala.vru.ac.ir/article_14591_7255b9cf0db6154ec39af397e9141d48.pdf