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On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification

  • R. Andreani
  • J. M. Martinez
  • M. L. Schuverdt
Technical Note

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 

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References

  1. Qi, L., Wei, Z. 2000On the Constant Positive Linear Dependence Condition and Its Application to SQP MethodsSIAM Journal on Optimization10963981Google Scholar
  2. Bertsekas, DP 1999Nonlinear Programming2Athena ScientificBelmont, MassachusettsGoogle Scholar
  3. Mangasarian, OL 1969Nonlinear ProgrammingMc Graw HillBombay, IndiaGoogle Scholar
  4. Hestenes, M.R 1975Optimization Theory : The Finite-Dimensional CaseJohn Wiley and SonsNew York, NYGoogle Scholar
  5. Bertsekas, D. P., Ozdaglar, A. E. 2002Pseudonormality and a Lagrange Multiplier Theory for Constrained OptimizationJournal of Optimization Theory and Applications114287343Google Scholar
  6. Bertsekas, D. P., and Ozdaglar, A. E., The Relation between Pseudonormality and Quasiregularity in Constrained Optimization; see http://www.mit.edu: 8001//people/dimitrib/Quasiregularity.pdf.Google Scholar
  7. Mangasarian, O.L, Fromovitz, S. 1967The Fritz-John Necessary Optimality Conditions in Presence of Equality and Inequality ConstraintsJournal of Mathematical Analysis and Applications173747Google Scholar
  8. Rockafellar, R. T. 1993Lagrange Multipliers and OptimalitySIAM Review35183238Google Scholar
  9. Janin, R. 1984Directional Derivative of the Marginal Function in Nonlinear ProgrammingMathematical Programming Study21110126Google Scholar
  10. Panier, E.R, Tits, AL 1993On Combining Feasibility, Descent and Superlinear Convergence in Inequality Constrained OptimizationMathematical Programming59261276Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • R. Andreani
    • 1
  • J. M. Martinez
    • 2
  • M. L. Schuverdt
    • 3
  1. 1.Associate Professor, IMECC-UNICAMPCampinas SPBrazil
  2. 2.Professor, IMECC-UNICAMPCampinas SPBrazil
  3. 3.PhD Student,IMECC-UNICAMPCampinas SPBrazil

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