Variational analysis of a composite function: A formula for the lower second order epi-derivative
Alexander Davidovich Ioffe · Journal of Mathematical Analysis and Applications · 1991
An exact formula is established for the lower second order epi-derivative of a function of the form g(F(x)), where F is a smooth map from one Banach space into another and g is a convex function (generally, not everywhere finite). Unconstrained minimization of such functions typically arise as an equivalent (in one or another sense) reduction form for many important classes of constrained optimization problems. The formula is further applied to study epi-differentiability of the max-function ƒ(x) = max{ƒ(q, x):q ϵ Q}.