Taylor’s Formula for $C^{k,1} $ Functions
利用Clarke广义雅可比，为k阶导数局部Lipschitz的函数建立了泰勒公式，并给出了隐函数广义Hessian的微积分规则，进而推导了高阶最优性条件和拟凸函数的二阶刻画。
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.