Abstract
In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.
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Jahn, J., Rauh, R. Contingent epiderivatives and set-valued optimization. Mathematical Methods of Operations Research 46, 193–211 (1997). https://doi.org/10.1007/BF01217690
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DOI: https://doi.org/10.1007/BF01217690