Regularized Newton Methods for Minimizing Functions with Hölder Continuous Hessians
研究了用于无约束最小化二次可微（凸或非凸）目标函数的正则化二阶方法，这些方法在不同Hölder类中自动达到最佳全局复杂度估计，并引入了两种新的线搜索接受准则。
In this paper, we study the regularized second-order methods for unconstrained minimization of a twice-differentiable (convex or nonconvex) objective function. For the current function, these methods automatically achieve the best possible global complexity estimates among different Hölder classes containing the Hessian of the objective. We show that such methods for functional residual and for the norm of the gradient must be different. For development of the latter methods, we introduced two new line-search acceptance criteria, which can be seen as generalizations of the Armijo condition.