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A New Abadie-Type Constraint Qualification for General Optimization Problems

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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.

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Acknowledgements

The first-named author was partially supported by a Grant from Iran National Science Foundation (INSF, No. 97007967)

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Authors and Affiliations

  1. Iran National Science Foundation (INSF), P.O. Box: 15875-3939, Tehran, Iran

    M. Alavi Hejazi

  2. Department of Applied Mathematics and Computer Science, University of Isfahan, P.O. Box: 81745-163, Isfahan, Iran

    N. Movahedian

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  1. M. Alavi Hejazi
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  2. N. Movahedian
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Correspondence to N. Movahedian.

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Communicated by René Henrion.

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Hejazi, M.A., Movahedian, N. A New Abadie-Type Constraint Qualification for General Optimization Problems. J Optim Theory Appl 186, 86–101 (2020). https://doi.org/10.1007/s10957-020-01691-0

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