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A relaxed constant positive linear dependence constraint qualification and applications

Mathematical Programming volume 135, pages255–273(2012)Cite this article

Abstract

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie’s constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

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Author information

Affiliations

  1. Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil

    Roberto Andreani

  2. Institute of Science and Technology, Federal University of São Paulo, São José dos Campos, SP, Brazil

    Gabriel Haeser

  3. CONICET, Department of Mathematics, FCE, University of La Plata, CP 172, 1900, La Plata, Bs. As., Argentina

    María Laura Schuverdt

  4. Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil

    Paulo J. S. Silva

Authors
  1. Roberto Andreani
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  2. Gabriel Haeser
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  3. María Laura Schuverdt
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  4. Paulo J. S. Silva
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Corresponding author

Correspondence to Paulo J. S. Silva.

Additional information

This work was supported by PRONEX-Optimization (PRONEX-CNPq/FAPERJ E-26/171.510/2006-APQ1), Fapesp (Grants 2006/53768-0 and 2009/09414-7) and CNPq (Grants 300900/2009-0, 303030/2007-0 and 474138/2008-9).

The second author would like to acknowledge that he was a research assistant at the University of São Paulo while this work was carried out.

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Andreani, R., Haeser, G., Schuverdt, M.L. et al. A relaxed constant positive linear dependence constraint qualification and applications. Math. Program. 135, 255–273 (2012). https://doi.org/10.1007/s10107-011-0456-0

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Keywords

  • Nonlinear programming
  • Constraint qualifications
  • Augmented Lagrangian
  • Error bound property

Mathematics Subject Classification (2000)

  • 90C30
  • 49K99
  • 65K05