Abstract
In this paper, we mainly study concepts of Abadie constraint qualification and strong Abadie constraint qualification for a convex constraint system defined by a closed convex multifunction and a closed convex subset. These concepts can cover Abadie constraint qualifications for the feasible region of convex optimization problem and the convex multifunction. Several characterizations for these Abadie constraint qualifications are also provided. As applications, we use these Abadie constraint qualifications to characterize calmness properties of the convex constraint system.
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Acknowledgements
The authors wish to thank the referee for many valuable comments which help us to reconstruct the counterexample in Remark 3.3 and improve the original presentation of this paper. The research of the first author was supported by the National Natural Science Foundation of P. R. China (Grant 11401518) and the Fok Ying-Tung Education Foundation (Grant 151101). The second author was partially supported by the Grant MOST 105-2115-M-039-002-MY3.
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Communicated by Asen L. Dontchev.
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Wei, Z., Yao, JC. Abadie Constraint Qualifications for Convex Constraint Systems and Applications to Calmness Property. J Optim Theory Appl 174, 388–407 (2017). https://doi.org/10.1007/s10957-017-1115-2
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DOI: https://doi.org/10.1007/s10957-017-1115-2