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A Relaxed Constant Positive Linear Dependence Constraint Qualification for Mathematical Programs with Equilibrium Constraints

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Abstract

We introduce a relaxed version of the constant positive linear dependence constraint qualification for mathematical programs with equilibrium constraints (MPEC). This condition is weaker but easier to check than the MPEC constant positive linear dependence constraint qualification, and stronger than the MPEC Abadie constraint qualification (thus, it is an MPEC constraint qualification for M-stationarity). Neither the new constraint qualification implies the MPEC generalized quasinormality, nor the MPEC generalized quasinormality implies the new constraint qualification. The new one ensures the validity of the local MPEC error bound under certain additional assumptions. We also have improved some recent results on the existence of a local error bound in the standard nonlinear program.

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Acknowledgements

The authors are grateful to two anonymous referees for insightful comments and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Vinh University, Vinh, Nghe An, Vietnam

    Nguyen Huy Chieu

  2. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    Gue Myung Lee

Authors
  1. Nguyen Huy Chieu
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  2. Gue Myung Lee
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Corresponding author

Correspondence to Gue Myung Lee.

Additional information

The first author was partially supported by the National Foundation for Science & Technology Development (Vietnam).

The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0018619).

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Chieu, N.H., Lee, G.M. A Relaxed Constant Positive Linear Dependence Constraint Qualification for Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl 158, 11–32 (2013). https://doi.org/10.1007/s10957-012-0227-y

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  • DOI: https://doi.org/10.1007/s10957-012-0227-y

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