Newton Differentiability of Convex Functions in Normed Spaces and of a Class of Operators
研究了无穷维空间中凸函数的牛顿可微性与Bouligand可微性及次微分上半连续性的关系，并构造了一类非线性算子的牛顿导数。
Newton differentiability is an important concept for analyzing generalized Newton methods for nonsmooth equations. In this work, for a convex function defined on an infinite-dimensional space, we discuss the relation between Newton and Bouligand differentiability and upper semicontinuity of its subdifferential. We also construct a Newton derivative of an operator of the form $(Fx)(p) = f(x,p)$ for general nonlinear operators $f$ that possess a Newton derivative with respect to $x$ and also for the case where $f$ is convex in $x$.