A vector forward mode of automatic differentiation for generalized derivative evaluation

Numerical methods for non-smooth equation-solving and optimization often require generalized derivative information in the form of elements of the Clarke Jacobian or the B-subdifferential. It is shown here that piecewise differentiable functions are lexicographically smooth in the sense of Nesterov, and that lexicographic derivatives of these functions comprise a particular subset of both the B-subdifferential and the Clarke Jacobian. Several …