TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS

TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS

Autor Andreani, Roberto Google Scholar
Haeser, Gabriel Autor UNIFESP Google Scholar
Laura Schuverdt, Maria Google Scholar
Silva, Paulo J. S. Google Scholar
Instituição Universidade Estadual de Campinas (UNICAMP)
Universidade Federal de São Paulo (UNIFESP)
Natl Univ La Plata
Universidade de São Paulo (USP)
Resumo 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.
Assunto constraint qualifications
error bound
algorithmic convergence
Idioma Inglês
Financiador Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Número do financiamento CNPq: E-26/171.510/2006-APQ1
FAPESP: 2006/53768-0
FAPESP: 2009/09414-7
FAPESP: 2010/19720-5
CNPq: 300900/2009-0
CNPq: 303030/2007-0
CNPq: 305740/2010-5
CNPq: 474138/2008-9
Data 2012-01-01
Publicado em Siam Journal On Optimization. Philadelphia: Siam Publications, v. 22, n. 3, p. 1109-1135, 2012.
ISSN 1052-6234 (Sherpa/Romeo, fator de impacto)
Editor Siam Publications
Extensão 1109-1135
Fonte http://dx.doi.org/10.1137/110843939
Direito de acesso Acesso aberto Open Access
Tipo Artigo
Web of Science WOS:000310214800019
URI http://repositorio.unifesp.br/handle/11600/34361

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