A cone-continuity constraint qualification and algorithmic consequences

PRONEX - PROGRAMA DE APOIO A NÚCLEOS DE EXCELÊNCIAFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOREvery local minimizer of a smooth constrained optimization problem satisfies the sequential approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called strict constraint qualifications (SCQs). In this paper we define a cone-continuity property (CCP) that will be shown to be the weakest possible SCQ. Its relation to other constraint qualifications will also be clarified. In particular, it will be proved that CCP is strictly weaker than the constant positive generator constraint qualification.Every local minimizer of a smooth constrained optimization problem satisfies the sequential approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called strict constraint qualifications (SCQs). In this paper we define a cone-continuity property (CCP) that will be shown to be the weakest possible SCQ. Its relation to other constraint qualifications will also be clarified. In particular, it will be proved that CCP is strictly weaker than the constant positive generator constraint qualification26196110PRONEX - PROGRAMA DE APOIO A NÚCLEOS DE EXCELÊNCIAFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORPRONEX - PROGRAMA DE APOIO A NÚCLEOS DE EXCELÊNCIAFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIORE-26/111.449/2010-APQ12013/07375-0; 2012/20339-0; 2013/05475-7304618/2013-6; 482549/2013-0; 303750/2014-6; 303013/2013-3sem informaçã

A Cone-continuity Constraint Qualification And Algorithmic Consequences

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Every local minimizer of a smooth constrained optimization problem satisfies the sequential approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called strict constraint qualifications (SCQs). In this paper we define a cone-continuity property (CCP) that will be shown to be the weakest possible SCQ. Its relation to other constraint qualifications will also be clarified. In particular, it will be proved that CCP is strictly weaker than the constant positive generator constraint qualification.26196110PRONEX-Optimization [PRONEX-CNPq/FAPERJ E-26/111.449/2010-APQ1]CEPID-CeMEAI [FAPESP 2013/07375-0]CNPq [304618/2013-6, 482549/2013-0, 303750/2014-6, 303013/2013-3]FAPESP [2012/20339-0, 2013/05475-7]CAPESNational Project on Industrial MathematicsConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES