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Two new weak constraint qualifications and applications

Roberto Andreani (andreani***at***ime.unicamp.br)
Gabriel Haeser (gabriel.haeser***at***unifesp.br)
María Laura Schuverdt (schuverd***at***mate.unlp.edu.ar)
Paulo J. S. Silva (pjssilva***at***ime.usp.br)

Abstract: We present two new constraint qualifications (CQ) that are weaker than the recently introduced Relaxed Constant Positive Linear Depen- dence (RCPLD) constraint qualification. RCPLD is based on the assump- tion 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 constraint qual- ification, that we call Constant Rank of the Subspace Component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, like local stability and the validity of an error bound. We also introduce an even weaker CQ, called Constant Positive Generator (CPG), that can re- place RCPLD in the analysis of the global convergence of algorithms. We close this work extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: SQP, augmented Lagrangians, interior point algorithms, and inexact restoration.

Keywords: constraint qualifications, error bound, nonlinear optimization, algorithmic convergence

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Instituto de Matemática e Estatística, Universidade de São Paulo, July, 2011

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Entry Submitted: 07/20/2011
Entry Accepted: 07/20/2011
Entry Last Modified: 02/13/2012

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