Contingent Epiderivatives and Set-Valued Optimization - Jahn, Johannes; Rauh, R. (Mathematical Methods of Operations Research, 1997)
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.
UnivIS-Import:2015-03-05:Pub.1997.nat.dma.pama21.contin
Keywords: Convex and set-valued analysis; Optimality conditions; Vector optimization