Eberhard, A.Pearce, C.Qi, L.Teo, K.Yang, X.2007-05-162007-05-162005Applied optimization - Optimization and control with applications, 2005 / Qi, L., Teo, K., Yang, X. (ed./s), pp.35-1000387242546http://hdl.handle.net/2440/30455The original publication is available at www.springerlink.comThe graphical derivative and the coderivative when applied to the proximal subdifferential are in general not generated by a set of linear operators Nevertheless we find that in directions at which the subject (or subhessian) is supported, in a rank-1 sense, we have these supported operators interpolating the contingent cone. Thus under a prox-regularity assumption we are able to make a selection from the contingent graphical derivative in certain directions, using the exposed facets of a convex set of symmetric matrices. This allows us to make a comparison between some optimality conditions. A nonsmooth formulation of a standard smooth mathematical programming problem is used to derive a novel set of sufficient optimality conditions.enBook chapter002005256710.1007/0-387-24255-4_253543