Taylor’s Formula for $C^{k,1} $ Functions
Dinh The Luc · SIAM Journal on Optimization · 1995
In this paper, using Clarke’s generalized Jacobian we establish Taylor’s formula for functions whose kth order derivatives are locally Lipschitz. A calculus rule for generalized Hessian of implicit functions is presented. The results are then applied to derive high-order optimality conditions and second-order characterizations of quasiconvex functions.