@article {
author = {Mohebi, A. and Mohebi, H.},
title = {Some relations between ε-directional derivative and ε-generalized weak subdifferential},
journal = {Wavelet and Linear Algebra},
volume = {2},
number = {1},
pages = {65-80},
year = {2015},
publisher = {Vali-e-Asr university of Rafsanjan},
issn = {2383-1936},
eissn = {2476-3926},
doi = {},
abstract = {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.},
keywords = {Non-convex optimization,"-directional derivative},
url = {http://wala.vru.ac.ir/article_14591.html},
eprint = {http://wala.vru.ac.ir/article_14591_7255b9cf0db6154ec39af397e9141d48.pdf}
}