Two new weak constraint qualifications and applications

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major o...

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Autores principales:	Andreani, Roberto, Haeser, Gabriel, Schuverdt, María Laura, Silva, Paulo J. S.
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2012
Materias:	Ciencias Exactas Matemática Algorithmic convergence Constraint qualifications Error bound
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/96342 https://ri.conicet.gov.ar/11336/80535 https://epubs.siam.org/doi/10.1137/110843939
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-96342
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Ciencias Exactas Matemática Algorithmic convergence Constraint qualifications Error bound
spellingShingle	Ciencias Exactas Matemática Algorithmic convergence Constraint qualifications Error bound Andreani, Roberto Haeser, Gabriel Schuverdt, María Laura Silva, Paulo J. S. Two new weak constraint qualifications and applications
topic_facet	Ciencias Exactas Matemática Algorithmic convergence Constraint qualifications Error bound
description	We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.
format	Articulo Articulo
author	Andreani, Roberto Haeser, Gabriel Schuverdt, María Laura Silva, Paulo J. S.
author_facet	Andreani, Roberto Haeser, Gabriel Schuverdt, María Laura Silva, Paulo J. S.
author_sort	Andreani, Roberto
title	Two new weak constraint qualifications and applications
title_short	Two new weak constraint qualifications and applications
title_full	Two new weak constraint qualifications and applications
title_fullStr	Two new weak constraint qualifications and applications
title_full_unstemmed	Two new weak constraint qualifications and applications
title_sort	two new weak constraint qualifications and applications
publishDate	2012
url	http://sedici.unlp.edu.ar/handle/10915/96342 https://ri.conicet.gov.ar/11336/80535 https://epubs.siam.org/doi/10.1137/110843939
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bdutipo_str	Repositorios
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Two new weak constraint qualifications and applications

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