Abstract We consider the optimal value function of a parametric optimization problem. A large number publications have been dedicated to study continuity and differentiability properties function. However, aspect works in current literature has mostly limited first order analysis, with focus on estimates its directional derivatives subdifferentials, given that is typically nonsmooth. With progr...

New elements of calculus on a complete real closed non-Archimedean field extension F of the real numbers R will be presented. It is known that the total disconnectedness of F in the topology induced by the order makes the usual (topological) notions of continuity and differentiability too weak to extend real calculus results to F . In this paper, we introduce new stronger concepts of continuity...

We study Lipschitz differentiability spaces, a class of metric measure spaces introduced by Cheeger in [8]. We show that if an Ahlfors regular Lipschitz differentiability space has charts of maximal dimension, then, at almost every point, all its tangents are uniformly rectifiable. In particular, at almost every point, such a space admits a tangent that is isometric to a finite-dimensional Bana...

adomian decomposition method has been applied to solve many functional equations so far. in this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. we interpret a fuzzy differential equation by using the strongly generalized differentiability. also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

We consider optimal control problems governed by nonlinear hyperbolic conservation laws at junctions and analyze in particular the Fréchet-differentiability of the reduced objective functional. This is done by showing that the control-to-state mapping of the considered problems satisfies a generalized notion of differentiability. We consider both, the case where the controls are the initial and...

We revisit some basic concepts and ideas of the classical differential calculus convex analysis extending them to a broader frame. reformulate generalize notion Gateaux differentiability propose new notions generalized derivative subdifferential in an arbitrary topological vector space. Meaningful examples preserving key properties original are provided.