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dc.contributor.CRUESPUNIVERSIDADE ESTADUAL DE CAMPINASpt_BR
dc.contributor.authorunicampAndreani, Roberto-
dc.typeArtigopt_BR
dc.titleA sequential optimality condition related to the quasi-normality constraint qualification and its algorithmic consequencespt_BR
dc.contributor.authorAndreani, Roberto-
dc.contributor.authorFazzio, Nadia S.-
dc.contributor.authorSchuverdt, Maria L.-
dc.contributor.authorSecchin, Leonardo D.-
dc.subjectLagrangiano aumentadopt_BR
dc.subject.otherlanguageAugmented lagrangianpt_BR
dc.description.abstractIn the present paper, we prove that the augmented Lagrangian method converges to KKT points under the quasi-normality constraint qualification, which is associated with the external penalty theory. An interesting consequence is that the Lagrange multiplier estimates computed by the method remain bounded in the presence of the quasi-normality condition. In order to establish a more general convergence result, a new sequential optimality condition for smooth constrained optimization, called PAKKT, is defined. The new condition takes into account the sign of the dual sequence, constituting an adequate sequential counterpart to the (enhanced) Fritz John necessary optimality conditions proposed by Hestenes, and later extensively treated by Bertsekas. PAKKT points are substantially better than points obtained by the classical approximate KKT (AKKT) condition, which has been used to establish theoretical convergence results for several methods. In particular, we present a simple problem with complementarity constraints such that all its feasible points are AKKT, while only the solutions and a pathological point are PAKKT. This shows the efficiency of the methods that reach PAKKT points, particularly the augmented Lagrangian algorithm, in such problems. We also provide the appropriate strict constraint qualification associated with the PAKKT sequential optimality condition, called PAKKT-regular, and we prove that it is strictly weaker than both quasi-normality and the cone continuity property. PAKKT-regular connects both branches of these independent constraint qualifications, generalizing all previous theoretical convergence results for the augmented Lagrangian method in the literaturept_BR
dc.relation.ispartofSIAM journal on optimizationpt_BR
dc.relation.ispartofabbreviationSIAM j. optim.pt_BR
dc.publisher.cityPhiladelphia, PApt_BR
dc.publisher.countryEstados Unidospt_BR
dc.publisherSociety for Industrial and Applied Mathematicspt_BR
dc.date.issued2019-
dc.language.isoengpt_BR
dc.description.volume29pt_BR
dc.description.issuenumber1pt_BR
dc.description.firstpage743pt_BR
dc.description.lastpage766pt_BR
dc.rightsAbertopt_BR
dc.sourceWOSpt_BR
dc.identifier.issn1052-6234pt_BR
dc.identifier.eissn1095-7189pt_BR
dc.identifier.doi10.1137/17M1147330pt_BR
dc.identifier.urlhttps://epubs.siam.org/doi/10.1137/17M1147330pt_BR
dc.description.sponsorshipCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQpt_BR
dc.description.sponsorshipFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESPpt_BR
dc.description.sponsordocumentnumber303013/2013-3pt_BR
dc.description.sponsordocumentnumber303013/2013-3; 2013/05475-7pt_BR
dc.date.available2020-06-03T19:01:38Z-
dc.date.accessioned2020-06-03T19:01:38Z-
dc.description.provenanceSubmitted by Mariana Aparecida Azevedo (mary1@unicamp.br) on 2020-06-03T19:01:38Z No. of bitstreams: 0. Added 1 bitstream(s) on 2020-09-03T11:55:36Z : No. of bitstreams: 1 000462593800029.pdf: 750331 bytes, checksum: 0dcaeab8a43be06da76f07e422125b8f (MD5)en
dc.description.provenanceMade available in DSpace on 2020-06-03T19:01:38Z (GMT). No. of bitstreams: 0 Previous issue date: 2019en
dc.identifier.urihttp://repositorio.unicamp.br/jspui/handle/REPOSIP/342610-
dc.contributor.departmentDepartamento de Matemática Aplicadapt_BR
dc.contributor.unidadeInstituto de Matemática, Estatística e Computação Científicapt_BR
dc.subject.keywordGlobal convergencept_BR
dc.subject.keywordConstraint qualificationspt_BR
dc.subject.keywordQuasi-normalitypt_BR
dc.subject.keywordSequential optimality conditionspt_BR
dc.identifier.source000462593800029pt_BR
dc.creator.orcid0000-0003-2031-4325pt_BR
dc.type.formArtigopt_BR
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