Continuous approximations to generalized jacobians

Here we discuss approximations to the Clarke generalized Jacobian of Lipschitz mappings from ℝ n , to ℝ m . A calculus for such approximations is outlined for both inner and outer compositions of Lipschitz mappings and continuously differentiable mappings. Typical examples of the approximations are presented. For real-valued Lipschitz functions these approximations reduce to approximations to the Clarke subdifferential. Applications of such approximations are outlined