Interior sphere condition for the graph of a multifunction
By introducing the notion of proximal-pseudo-differentiability for multifunctions, the authors prove the equivalence between the pointwise interior sphere condition of a multifunction and the interior sphere condition of its graph. This equivalence will open an ability for extending the semiconcavity results by \textit{C. Nour} and \textit{R. J. Stern} [Syst. Control Lett. 57, No. 10, 863--866 (2008; Zbl 1162.49021)] to the nonlinear case.
scientific article; zbMATH DE number 6345547
scientific article