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Paper   IPM / M / 14992
School of Mathematics
  Title:   Optimality conditions in optimization problems with convex feasible set using convexificators
  Author(s): 
1.  Majid Soelimani-Damaneh
2.  Moslem Zamani (Joint with A. Kabgani)
  Status:   Published
  Journal: Math. Meth. Oper. Res.
  Vol.:  86
  Year:  2017
  Pages:   103-121
  Supported by:  IPM
  Abstract:
n this paper, we consider a nonsmooth optimization problem with a convex feasible set described by constraint functions which are neither convex nor differentiable nor locally Lipschitz necessarily. Utilizing upper regular convexificators, we characterize the normal cone of the feasible set and derive KKT type necessary and sufficient optimality conditions. Under some assumptions, we show that the set of KKT multipliers is bounded. We also characterize the set of optimal solutions and introduce a linear approximation corresponding to the original problem which is useful in checking optimality. The obtained outcomes extend various results existing in the literature to a more general setting.

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