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A New Abadie-Type Constraint Qualification for General Optimization Problems

Author

Listed:
  • M. Alavi Hejazi

    (Iran National Science Foundation (INSF))

  • N. Movahedian

    (University of Isfahan)

Abstract

A non-Lipschitz version of the Abadie constraint qualification is introduced for a nonsmooth and nonconvex general optimization problem. The relationship between the new Abadie-type constraint qualification and the local error bound property is clarified. Also, a necessary optimality condition, based on the pseudo-Jacobians, is derived under the Abadie constraint qualification. Moreover, some examples are given to illustrate the obtained results.

Suggested Citation

  • M. Alavi Hejazi & N. Movahedian, 2020. "A New Abadie-Type Constraint Qualification for General Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 86-101, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01691-0
    DOI: 10.1007/s10957-020-01691-0
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    References listed on IDEAS

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    1. M. Alavi Hejazi & N. Movahedian & S. Nobakhtian, 2018. "On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 778-799, December.
    2. V. Jeyakumar & D. T. Luc, 1999. "Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 599-621, June.
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