Concise representation of generalised gradients

Computing the generalised gradient directly using its standard definition can involve forming the convex hull of a very large number of vectors. Here an alternative concise parametrization is developed for the generalised gradient of the signed rank regression family of objective functions, a class of piecewise linear functions which includes both convex and nonconvex members. The approach uses the geometry of the epigraph explicitly and this suggests extensions to more general functions. A nondegeneracy condition is assumed which is natural in optimization problems.