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Abadie Constraint Qualifications for Convex Constraint Systems and Applications to Calmness Property

Author

Listed:
  • Zhou Wei

    (Yunnan University)

  • Jen-Chih Yao

    (China Medical University
    Kaohsiung Medical University)

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.

Suggested Citation

  • Zhou Wei & Jen-Chih Yao, 2017. "Abadie Constraint Qualifications for Convex Constraint Systems and Applications to Calmness Property," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 388-407, August.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:2:d:10.1007_s10957-017-1115-2
    DOI: 10.1007/s10957-017-1115-2
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    Cited by:

    1. Zhou Wei & Christiane Tammer & Jen-Chih Yao, 2021. "Characterizations for Strong Abadie Constraint Qualification and Applications to Calmness," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 1-18, April.

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