A simple way of defining a generalized derivative for arbitrary functions is introduced.Its main feature lies in its coincidence with the usual derivative when the function is differentiable, a property which is not shared by the strict derivative of F. Clarke.Calculus rules are presented; in particular, functions satisfying a regularity condition weaker than a Lipschitzian property are shown to verify a chain rule.Applications to optimization are pointed out.
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Michel et al. (1992) studied this question.