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New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions

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Abstract

In this paper, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian–Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the existence of local error bounds for the system of inequalities and equalities. We further extend the new result to the mathematical programs with equilibrium constraints. In particular, we show that the MPEC relaxed (or enhanced relaxed) constant positive linear dependence condition implies the existence of local error bounds for the mixed complementarity system.

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Acknowledgments

The authors would like to thank the two anonymous referees for their helpful and valuable comments and suggestions. The authors are also grateful to Professor Jane J. Ye at University of Victoria for her helpful discussions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Lei Guo

  2. Sino-US Global Logistics Institute, Shanghai Jiao Tong University, Shanghai, 200030, China

    Lei Guo

  3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3P4, Canada

    Lei Guo & Jin Zhang

  4. School of Management, Shanghai University, Shanghai,  200444, China

    Gui-Hua Lin

Authors
  1. Lei Guo
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  2. Jin Zhang
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  3. Gui-Hua Lin
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Correspondence to Lei Guo.

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Guo, L., Zhang, J. & Lin, GH. New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions. J Optim Theory Appl 163, 737–754 (2014). https://doi.org/10.1007/s10957-013-0510-6

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  • DOI: https://doi.org/10.1007/s10957-013-0510-6

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