Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints

Detalhes bibliográficos
Autor(a) principal: Villanueva, Fabiola Roxana
Data de Publicação: 2022
Outros Autores: Oliveira, Valeriano Antunes de [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s10957-022-02055-6
http://hdl.handle.net/11449/240379
Resumo: This work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional and abstract forms. The functional constraints are described by means of both inequalities and equalities. The abstract constraint is expressed through a closed and convex set with a nonempty interior. Necessary optimality conditions are derived, given in a multiplier rule structure involving the gH-gradient of the interval objective function along with the (classical) gradients of the constraint functions and the normal cone to the set related to the abstract constraint. The main tool is a specification of the Dubovitskii–Milyutin formalism. We defined an appropriated notion of directions of decrease to an interval-valued function, using the lower–upper partial ordering of the interval space (LU order).
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spelling Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract ConstraintsDubovitskii–Milyutin formalismInterval optimizationKarush–Kuhn–TuckerNecessary optimality conditionsThis work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional and abstract forms. The functional constraints are described by means of both inequalities and equalities. The abstract constraint is expressed through a closed and convex set with a nonempty interior. Necessary optimality conditions are derived, given in a multiplier rule structure involving the gH-gradient of the interval objective function along with the (classical) gradients of the constraint functions and the normal cone to the set related to the abstract constraint. The main tool is a specification of the Dubovitskii–Milyutin formalism. We defined an appropriated notion of directions of decrease to an interval-valued function, using the lower–upper partial ordering of the interval space (LU order).Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidad Mayor de San Andrés, La PazSão Paulo State University, São PauloSão Paulo State University, São PauloFAPESP: 2013/07375-0CNPq: 305786/2018-0CAPES: Finance code 001Universidad Mayor de San AndrésUniversidade Estadual Paulista (UNESP)Villanueva, Fabiola RoxanaOliveira, Valeriano Antunes de [UNESP]2023-03-01T20:14:35Z2023-03-01T20:14:35Z2022-09-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article896-923http://dx.doi.org/10.1007/s10957-022-02055-6Journal of Optimization Theory and Applications, v. 194, n. 3, p. 896-923, 2022.1573-28780022-3239http://hdl.handle.net/11449/24037910.1007/s10957-022-02055-62-s2.0-85133293051Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Optimization Theory and Applicationsinfo:eu-repo/semantics/openAccess2023-03-01T20:14:35Zoai:repositorio.unesp.br:11449/240379Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:10:34.071947Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
title Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
spellingShingle Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
Villanueva, Fabiola Roxana
Dubovitskii–Milyutin formalism
Interval optimization
Karush–Kuhn–Tucker
Necessary optimality conditions
title_short Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
title_full Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
title_fullStr Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
title_full_unstemmed Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
title_sort Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
author Villanueva, Fabiola Roxana
author_facet Villanueva, Fabiola Roxana
Oliveira, Valeriano Antunes de [UNESP]
author_role author
author2 Oliveira, Valeriano Antunes de [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidad Mayor de San Andrés
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Villanueva, Fabiola Roxana
Oliveira, Valeriano Antunes de [UNESP]
dc.subject.por.fl_str_mv Dubovitskii–Milyutin formalism
Interval optimization
Karush–Kuhn–Tucker
Necessary optimality conditions
topic Dubovitskii–Milyutin formalism
Interval optimization
Karush–Kuhn–Tucker
Necessary optimality conditions
description This work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional and abstract forms. The functional constraints are described by means of both inequalities and equalities. The abstract constraint is expressed through a closed and convex set with a nonempty interior. Necessary optimality conditions are derived, given in a multiplier rule structure involving the gH-gradient of the interval objective function along with the (classical) gradients of the constraint functions and the normal cone to the set related to the abstract constraint. The main tool is a specification of the Dubovitskii–Milyutin formalism. We defined an appropriated notion of directions of decrease to an interval-valued function, using the lower–upper partial ordering of the interval space (LU order).
publishDate 2022
dc.date.none.fl_str_mv 2022-09-01
2023-03-01T20:14:35Z
2023-03-01T20:14:35Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s10957-022-02055-6
Journal of Optimization Theory and Applications, v. 194, n. 3, p. 896-923, 2022.
1573-2878
0022-3239
http://hdl.handle.net/11449/240379
10.1007/s10957-022-02055-6
2-s2.0-85133293051
url http://dx.doi.org/10.1007/s10957-022-02055-6
http://hdl.handle.net/11449/240379
identifier_str_mv Journal of Optimization Theory and Applications, v. 194, n. 3, p. 896-923, 2022.
1573-2878
0022-3239
10.1007/s10957-022-02055-6
2-s2.0-85133293051
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal of Optimization Theory and Applications
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 896-923
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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