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An extremal vector problem under inclusion constraints via radial epi-derivatives

. In this paper, we consider an extremal problem under inclusions constraints. Based on recent semicontinuous epi-derivatives results, we establish necessary and sufﬁcient optimality conditions of Fermat type for this problem. We do not require any differentiability or regularity condition on the objective function. We ﬁnally give some examples of functions to which our results may be applied.