EPIDERIVATIVES WITH RESPECT TO HALF-SPACES
Elvira Hern ́andez, Luis Rodr ́lguez-Mar ́ln, Miguel Sama · Taiwanese Journal of Mathematics · 2008
In this paper we extend some results given in [L. Rodr\hspace{-0.02cm}{\'{\hspace{-0.09cm}\tiny l}}\hspace{0.02cm}guez-Mar\hspace{-0.02cm}{\'{\hspace{-0.09cm}\tiny l}}\hspace{0.02cm}n, M. Sama, $\tau^{w}$% -contingent epiderivatives in reflexive spaces, \textit{Nonlinear Analysis}, {\bf 68} (2008), 3780-3788]. Following the same approach, we associate a set-valued optimization problem with a family of simpler problems by using a decoupling of the ordering cone into half-spaces. In this context we give necessary and sufficient optimality conditions in terms of epiderivatives with respect to half-spaces. Moreover we obtain computation formulas for these conditions in term of derivatives of scalar set-valued maps.