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Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property

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Abstract

This paper studies the system of constraint qualifications tailored for mathematical programs with equilibrium constraints. The main focuses are on the relations among them and their local preservation property. After giving a relaxed version of the constant positive linear dependence constraint qualification for mathematical programs with equilibrium constraints, we establish some new relations among the tailored constraint qualifications. Then, we investigate their local preservation property. Finally, we present several results on the isolatedness of local minimizers. The paper contains some proof techniques that seem to be new in the literature of mathematical programs with equilibrium constraints. The obtained results complement and improve some recent ones in this direction.

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Acknowledgments

The authors would like to express their sincere thanks to three anonymous referees for their helpful suggestions and constructive comments. The first author was 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. 2012-0006236).

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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, Pusan, 608-737, Korea

    Gue Myung Lee

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  1. Nguyen Huy Chieu
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  2. Gue Myung Lee
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Correspondence to Gue Myung Lee.

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Communicated by Patrice Marcotte.

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Chieu, N.H., Lee, G.M. Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property. J Optim Theory Appl 163, 755–776 (2014). https://doi.org/10.1007/s10957-014-0546-2

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  • DOI: https://doi.org/10.1007/s10957-014-0546-2

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