Calmness and Exact Penalization in Constrained Scalar Set-Valued Optimization

In this paper, we study a class of constrained scalar set-valued optimization problems, which includes scalar optimization problems with cone constraints as special cases. We introduce (local) calmness of order α for this class of constrained scalar set-valued optimization problems. We show that the (local) calmness of order α is equivalent to the existence of a (local) exact set-valued penalty map.

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