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On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians

Author

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  • M. Alavi Hejazi

    (University of Isfahan)

  • N. Movahedian

    (University of Isfahan)

  • S. Nobakhtian

    (University of Isfahan
    Institute for Research in Fundamental Sciences (IPM))

Abstract

A nonsmooth and nonconvex general optimization problem is considered. Using the idea of pseudo-Jacobians, nonsmooth versions of the Robinson and Mangasarian–Fromovitz constraint qualifications are defined and relationships between them and the local error bound property are investigated. A new necessary optimality condition, based on the pseudo-Jacobians, is derived under the local error bound constraint qualification. These results are applied for computing and estimating the Fréchet and limiting subdifferentials of value functions. Moreover, several examples are provided to clarify the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1336-z
    DOI: 10.1007/s10957-018-1336-z
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    References listed on IDEAS

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    1. A. M. Bagirov & L. Jin & N. Karmitsa & A. Al Nuaimat & N. Sultanova, 2013. "Subgradient Method for Nonconvex Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 416-435, May.
    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.
    3. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 147-163, July.
    4. A. Moldovan & L. Pellegrini, 2009. "On Regularity for Constrained Extremum Problems. Part 2: Necessary Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 165-183, July.
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    Cited by:

    1. 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.

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