Necessary Optimality Conditions for Interval Optimization Problems with Functional and Abstract Constraints
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | |
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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808128474444988416 |