EPIDERIVATIVES WITH RESPECT TO HALF-SPACES

Abstract

In this paper we extend some results given in [L. Rodríguez-Marín, M. Sama, $\tau^{w}$-contingent epiderivatives in reflexive spaces, Nonlinear Analysis, {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.