The directional derivatives and subdifferentials of set-valued mappings are studied by scalarization approaches.With the help of the Gerstewizt function,the concepts of Michel-Penot directional derivatives and Michel-Penot subdifferentials of set-valued mappings are introduced.Their properties are studied and their calculus rules are established.As application,optimality conditions for unconstrained set-valued optimization problems are given by Michel-Penot subdifferentials.
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