
Journal of Convex Analysis 14 (2007), No. 2, 433454 Copyright Heldermann Verlag 2007 Infinite Dimensional Clarke Generalized Jacobian Zsolt Páles Institute of Mathematics, University of Debrecen, 4010 Debrecen Pf. 12, Hungary pales@math.klte.hu Vera Zeidan Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A. zeidan@math.msu.edu We extend for a locally Lipschitz function the notion of Clarke's generalized Jacobian to the setting where the domain lies in an infinite dimensional normed space. When the function is realvalued this notion reduces to the Clarke's generalized gradient. Using this extension, we obtain an exact smoothnonsmooth chain rule from which the sum rule and the product rule follow. Also an exact formula for the generalized Jacobian of piecewise differentiable functions will be provided. Keywords: Generalized Jacobian, chain rule, sum rule, piecewise smooth functions. MSC: 49A52, 58C20 [ Fulltextpdf (201 KB)] for subscribers only. 