Evaluation Complexity For Nonlinear Constrained Optimization Using Unscaled Kkt Conditions And High-order Models

dc.creatorBirgin
dc.creatorE. G.; Gardenghi
dc.creatorJ. L.; Martinez
dc.creatorJ. M.; Santos
dc.creatorS. A.; Toint
dc.creatorPh. L.
dc.date2016
dc.date2017-11-13T13:14:10Z
dc.date2017-11-13T13:14:10Z
dc.date.accessioned2018-03-29T05:52:01Z
dc.date.available2018-03-29T05:52:01Z
dc.identifierSiam Journal On Optimization. Siam Publications, v. 26, p. 951 - 967, 2016.
dc.identifier1052-6234
dc.identifier1095-7189
dc.identifierWOS:000386453800003
dc.identifier10.1137/15M1031631
dc.identifierhttp://epubs.siam.org/doi/abs/10.1137/15M1031631
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/327131
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1364156
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionThe evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an epsilon-approximate first-order critical point of the problem can be computed in order O(epsilon(1-2(p+1)/p)) evaluations of the problem's functions and their first p derivatives. This is achieved by using a two-phase algorithm inspired by Cartis, Gould, and Toint [SIAM J. Optim., 21 (2011), pp. 1721-1739; SIAM J. Optim., 23 (2013), pp. 1553-1574]. It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the epsilon-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
dc.description26
dc.description2
dc.description951
dc.description967
dc.descriptionBrazilian agency FAPESP [2010/10133-0, 2013/03447-6, 2013/05475-7, 2013/07375-0, 2013/23494-9]
dc.descriptionBrazilian agency CNPq [304032/2010-7, 309517/2014-1, 303750/2014-6, 490326/2013-7]
dc.descriptionBelgian National Fund for Scientific Research (FNRS)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.languageEnglish
dc.publisherSIAM Publications
dc.publisherPhiladelphia
dc.relationSIAM Journal on Optimization
dc.rightsaberto
dc.sourceWOS
dc.subjectNonlinear Programming
dc.subjectComplexity
dc.subjectApproximate Kkt Point
dc.titleEvaluation Complexity For Nonlinear Constrained Optimization Using Unscaled Kkt Conditions And High-order Models
dc.typeArtículos de revistas


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