On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification Technical Note DOI:
Cite this article as: Andreani, R., Martinez, J.M. & Schuverdt, M.L. J Optim Theory Appl (2005) 125: 473. doi:10.1007/s10957-004-1861-9 Abstract
The constant positive linear dependence (CPLD) condition for feasible points of nonlinear programming problems was introduced by Qi and Wei (Ref. 1) and used in the analysis of SQP methods. In that paper, the authors conjectured that the CPLD could be a constraint qualification. This conjecture is proven in the present paper. Moreover, it is shown that the CPLD condition implies the quasinormality constraint qualification, but that the reciprocal is not true. Relations with other constraint qualifications are given.
Keywords Nonlinear programming constraint qualifications CPLD condition quasinormality
This research has been supported by PRONEX-Optimization Grant 76.79.1008-00, by FAPESP Grants 01-04597-4 and 02-00832-1, and by CNPq. The authors are indebted to two anonymous referees for useful comments and to Prof. Liqun Qi for encouragement.
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