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Paper   IPM / M / 16545
School of Mathematics
  Title:   Robustness in nonsmooth nonconvex optimization problems
  Author(s):  Soghra Nobakhtian (Joint with F. Mashkoorzadeh and N. Movahedian)
  Status:   To Appear
  Journal: Positivity
  Supported by:  IPM
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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