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Robustness in Nonsmooth Nonconvex Optimization Problems

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Abstract

In this paper, the robust approach (the worst case approach) for nonsmooth nonconvex optimization problems with uncertainty data is studied. First various robust constraint qualifications are introduced based on the concept of tangential subdifferential. Further, robust necessary and sufficient optimality conditions are derived in the absence of the convexity of the uncertain sets and the concavity of the related functions with respect to the uncertain parameters. Finally, the results are applied to obtain the necessary and sufficient optimality conditions for robust weakly efficient solutions in multiobjective programming problems. In addition, several examples are provided to illustrate the advantages of the obtained outcomes.

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Acknowledgements

The third-named author was partially supported by a Grant from IPM (No. 99900416).

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, P.O. Box 81745-163, Isfahan, Iran

    F. Mashkoorzadeh, N. Movahedian & S. Nobakhtian

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    S. Nobakhtian

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  1. F. Mashkoorzadeh
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  3. S. Nobakhtian
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Correspondence to N. Movahedian.

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Mashkoorzadeh, F., Movahedian, N. & Nobakhtian, S. Robustness in Nonsmooth Nonconvex Optimization Problems. Positivity 25, 701–729 (2021). https://doi.org/10.1007/s11117-020-00783-5

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