On optimization via ϵ-generalized weak subdifferentials

© 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...

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Bibliographic Details
Main Authors: P. Cheraghi, A. P. Farajzadeh, S. Suantai
Format: Journal
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046352187&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/58812
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Institution: Chiang Mai University
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Summary:© 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.