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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Main Authors:	P. Cheraghi, A. P. Farajzadeh, S. Suantai
Format:	Journal
Published:	2018
Subjects:	Mathematics
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

id	th-cmuir.6653943832-58812
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spelling	th-cmuir.6653943832-588122018-09-05T04:32:52Z On optimization via ϵ-generalized weak subdifferentials P. Cheraghi A. P. Farajzadeh S. Suantai Mathematics © 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. 2018-09-05T04:32:52Z 2018-09-05T04:32:52Z 2018-04-01 Journal 16860209 2-s2.0-85046352187 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046352187&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58812
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics P. Cheraghi A. P. Farajzadeh S. Suantai On optimization via ϵ-generalized weak subdifferentials
description	© 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.
format	Journal
author	P. Cheraghi A. P. Farajzadeh S. Suantai
author_facet	P. Cheraghi A. P. Farajzadeh S. Suantai
author_sort	P. Cheraghi
title	On optimization via ϵ-generalized weak subdifferentials
title_short	On optimization via ϵ-generalized weak subdifferentials
title_full	On optimization via ϵ-generalized weak subdifferentials
title_fullStr	On optimization via ϵ-generalized weak subdifferentials
title_full_unstemmed	On optimization via ϵ-generalized weak subdifferentials
title_sort	on optimization via ϵ-generalized weak subdifferentials
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85046352187&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58812
_version_	1681425135341404160

On optimization via ϵ-generalized weak subdifferentials

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