Bài báo/NewspaperAuthors: V. Jeyakumar (1998)
The notion of approximate Jacobian matrices is introduced for a continuous vector valued map. It is shown, for instance, that the Clarke generalized Jacobian is an approximate
Jacobian for a locally Lipschitz map. The approach is based on the idea of convexificators of real valued functions. Mean value conditions for continuous vector-valued maps and Taylor’s expansions
for continuously Gˆateaux differentiable functions (i.e., C1-functions) are presented in terms of ap proximate Jacobians and approximate Hessians, respectively. Second-order necessary and sufficient
conditions for optimality and convexity of C1-functions are also given 
