TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS

TWO NEW WEAK CONSTRAINT QUALIFICATIONS and APPLICATIONS

Author Andreani, Roberto Google Scholar
Haeser, Gabriel Autor UNIFESP Google Scholar
Laura Schuverdt, Maria Google Scholar
Silva, Paulo J. S. Google Scholar
Institution Universidade Estadual de Campinas (UNICAMP)
Universidade Federal de São Paulo (UNIFESP)
Natl Univ La Plata
Universidade de São Paulo (USP)
Abstract 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.
Keywords constraint qualifications
error bound
algorithmic convergence
Language English
Sponsor Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Grant number 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
Date 2012-01-01
Published in Siam Journal On Optimization. Philadelphia: Siam Publications, v. 22, n. 3, p. 1109-1135, 2012.
ISSN 1052-6234 (Sherpa/Romeo, impact factor)
Publisher Siam Publications
Extent 1109-1135
Origin http://dx.doi.org/10.1137/110843939
Access rights Open access Open Access
Type Article
Web of Science ID WOS:000310214800019
URI http://repositorio.unifesp.br/handle/11600/34361

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