On optimization via ϵ-generalized weak subdifferentials

Abstract

© 2018 by the Mathematical Association of Thailand. All rights reserved. In this paper, we study ϵ-generalized weak subdifferential for functions defined on a real topological vector space. Some necessary and sufficient conditions for having nonempty ϵ-generalized weak subdifferential of a function are presented. The positively homogenous of the ϵ-generalized weak subdifferential operator is proved. A necessary and sufficient conditions for achieving a global minimum of a ϵ-generalized weak subdifferentiable function is stated. A link between sudifferential and Fréchet differential with ϵ-generalized weak subdifferential is established. Finally a result about the equality of the fuzzy sum rule inclusion is investigated.