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On the relationship between bilevel decomposition algorithms and direct interior-point methods

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dc.affiliation.dptoUC3M. Departamento de Estadísticaes
dc.contributor.authorMiguel, Angel Víctor de
dc.contributor.authorNogales Martín, Francisco Javier
dc.date.accessioned2006-11-09T10:55:52Z
dc.date.available2006-11-09T10:55:52Z
dc.date.issued2004-04
dc.description.abstractEngineers have been using bilevel decomposition algorithms to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upperlevel problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used bilevel decomposition algorithms may fail to converge even when the starting point is very close to the minimizer. In this paper, we establish a relationship between a particular bilevel decomposition algorithm, which only performs one iteration of an interior-point method when solving the subproblems, and a direct interior-point method, which solves the problem in its original (integrated) form. Using this relationship, we formally prove that the bilevel decomposition algorithm converges locally at a superlinear rate. The relevance of our analysis is that it bridges the gap between the incipient local convergence theory of bilevel decomposition algorithms and the mature theory of direct interior-point methods.en
dc.format.extent458031 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.repecws042509
dc.identifier.urihttps://hdl.handle.net/10016/213
dc.language.isoeng
dc.language.isoeng
dc.relation.ispartofseriesUC3M Working Papers. Statistics and Econometrics
dc.relation.ispartofseries2004-09
dc.rights.accessRightsopen access
dc.subject.ecienciaEstadística
dc.titleOn the relationship between bilevel decomposition algorithms and direct interior-point methodsen
dc.typeworking paper*
dspace.entity.typePublication
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