Let / be a function from rn to r . following the definitions of the generalized gradients proposed by clarke and xu yihong , respectively , we define the d - regular weak lipschitz function and propose a new generalized gradient as follows where d _ f ( x ; d ) is the directional derivative of / in the direction d at the point x , namely some properties are proposed 第二节引入基本定义和记号，在clarke和徐义红提出的各自的广义梯度的基础上，定义了一类d正则弱l函数，且提出了一个新的广义梯度。设f ： r ~ n r ，其广义梯度为其中为f在处沿方向d的方向导数，即并给出了若干性质定理。
