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2005-10-26Buch DOI: 10.18452/2544
On the Role of the Mangasarian-Fromovitz Constraint Qualification for Penalty-, Exact Penalty- and Lagrange Multiplier Methods
dc.contributor.authorGuddat, Jürgen
dc.contributor.authorVazquez, Francisco Guerra
dc.contributor.authorNowack, Dieter
dc.date.accessioned2017-06-15T17:30:13Z
dc.date.available2017-06-15T17:30:13Z
dc.date.created2005-10-26
dc.date.issued2005-10-26
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3196
dc.description.abstractIn this paper we consider three embeddings (one-parametric optimization problems) motivated by penalty, exact penalty and Lagrange multiplier methods. We give an answer to the question under which conditions these methods are successful with an arbitrarily chosen starting point. Using the theory of one-parametric optimization (the local structure of the set of stationary points and of the set of generalized critical points, singularities, structural stability, pathfollowing and jumps) the so-called Mangasarian-Fromovitz condition and its extension play an important role. The analysis shows us that the class of optimization problems for which we can surely find a stationary point using a pathfollowing procedure for the modified penalty and exact penalty embedding is much larger than the class where the Lagrange multiplier embedding is successful. For the first class, the objective may be a “really non-convex” function, but for the second one we are restricted to convex optimization problems. This fact was a surprise at least for the authors.eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.subject.ddc510 Mathematik
dc.titleOn the Role of the Mangasarian-Fromovitz Constraint Qualification for Penalty-, Exact Penalty- and Lagrange Multiplier Methods
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10051220
dc.identifier.doihttp://dx.doi.org/10.18452/2544
dc.subject.dnb27 Mathematik
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages24
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume1996
local.edoc.container-issue16
local.edoc.container-year1996
local.edoc.container-erstkatid2075199-0

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