Nonlinear duality and multiplier theorems

The main purpose of this paper is to extend the John theorem on nonlinear programming with inequality contraints and the Mangasarian-Fromovitz theorem on nonlinear programming with mixed constraints to any real normed linear space. In addition, for the John theorem assuming Frechet differentiability...

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Autores:: Azpeitia, Alfonso G.

Tipo de recurso:: Article of journal

Fecha de publicación:: 1987

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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spelling	Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Azpeitia, Alfonso G.61e20902-3080-4cc1-8a38-691fdccf239c3002019-06-28T11:17:55Z2019-06-28T11:17:55Z1987https://repositorio.unal.edu.co/handle/unal/42888http://bdigital.unal.edu.co/32986/The main purpose of this paper is to extend the John theorem on nonlinear programming with inequality contraints and the Mangasarian-Fromovitz theorem on nonlinear programming with mixed constraints to any real normed linear space. In addition, for the John theorem assuming Frechet differentiability, the standard conclusion that the multiplier vector is not zero is sharpened to the nonvanishing of the subvector of those components corresponding to the constraints which are not linear affine. The only tools used are generalizations of the duality theorem of linear programming, and hence of the Farkas lemma, to the case of a primal real linear space of any dimension with no topological restrictions. It is shown that these generalizations are direct consequence of the ordiry duality theorem of linear programming in finite dimension.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/32728Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 13-24 0034-7426Azpeitia, Alfonso G. (1987) Nonlinear duality and multiplier theorems. Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 13-24 0034-7426 .Nonlinear duality and multiplier theoremsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTJohn theoremnonlinear programmingtheorem Mangasarian-Fromovitzrestrictions mixedlinear spacefinite dimensionalORIGINAL32728-121128-1-PB.pdfapplication/pdf2650900https://repositorio.unal.edu.co/bitstream/unal/42888/1/32728-121128-1-PB.pdf2d1c70988a6f1265f8d5d89d551dd8c5MD51THUMBNAIL32728-121128-1-PB.pdf.jpg32728-121128-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5881https://repositorio.unal.edu.co/bitstream/unal/42888/2/32728-121128-1-PB.pdf.jpg572b7018b440b1a786644d4b9b8843cbMD52unal/42888oai:repositorio.unal.edu.co:unal/428882024-02-07 23:08:52.818Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv	Nonlinear duality and multiplier theorems
title	Nonlinear duality and multiplier theorems
spellingShingle	Nonlinear duality and multiplier theorems John theorem nonlinear programming theorem Mangasarian-Fromovitz restrictions mixed linear space finite dimensional
title_short	Nonlinear duality and multiplier theorems
title_full	Nonlinear duality and multiplier theorems
title_fullStr	Nonlinear duality and multiplier theorems
title_full_unstemmed	Nonlinear duality and multiplier theorems
title_sort	Nonlinear duality and multiplier theorems
dc.creator.fl_str_mv	Azpeitia, Alfonso G.
dc.contributor.author.spa.fl_str_mv	Azpeitia, Alfonso G.
dc.subject.proposal.spa.fl_str_mv	John theorem nonlinear programming theorem Mangasarian-Fromovitz restrictions mixed linear space finite dimensional
topic	John theorem nonlinear programming theorem Mangasarian-Fromovitz restrictions mixed linear space finite dimensional
description	The main purpose of this paper is to extend the John theorem on nonlinear programming with inequality contraints and the Mangasarian-Fromovitz theorem on nonlinear programming with mixed constraints to any real normed linear space. In addition, for the John theorem assuming Frechet differentiability, the standard conclusion that the multiplier vector is not zero is sharpened to the nonvanishing of the subvector of those components corresponding to the constraints which are not linear affine. The only tools used are generalizations of the duality theorem of linear programming, and hence of the Farkas lemma, to the case of a primal real linear space of any dimension with no topological restrictions. It is shown that these generalizations are direct consequence of the ordiry duality theorem of linear programming in finite dimension.
publishDate	1987
dc.date.issued.spa.fl_str_mv	1987
dc.date.accessioned.spa.fl_str_mv	2019-06-28T11:17:55Z
dc.date.available.spa.fl_str_mv	2019-06-28T11:17:55Z
dc.type.spa.fl_str_mv	Artículo de revista
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url	https://repositorio.unal.edu.co/handle/unal/42888 http://bdigital.unal.edu.co/32986/
dc.language.iso.spa.fl_str_mv	spa
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dc.relation.spa.fl_str_mv	http://revistas.unal.edu.co/index.php/recolma/article/view/32728
dc.relation.ispartof.spa.fl_str_mv	Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv	Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 13-24 0034-7426
dc.relation.references.spa.fl_str_mv	Azpeitia, Alfonso G. (1987) Nonlinear duality and multiplier theorems. Revista Colombiana de Matemáticas; Vol. 21, núm. 1 (1987); 13-24 0034-7426 .
dc.rights.spa.fl_str_mv	Derechos reservados - Universidad Nacional de Colombia
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dc.publisher.spa.fl_str_mv	Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution	Universidad Nacional de Colombia
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Nonlinear duality and multiplier theorems

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