SIAM Journal on Optimization, Volume 31, Issue 2, Page 1184-1214, January 2021.
This paper aims at developing two versions of the generalized Newton method to compute local minimizers for nonsmooth problems of unconstrained and constrained optimization that satisfy an important stability property known as tilt stability. We start with unconstrained minimization of continuously differentiable cost functions having Lipschitzian gradients and suggest two second-order algorithms of Newton type: one involving coderivatives of Lipschitzian gradient mappings, and the other based on graphical derivatives of the latter. Then we proceed with the propagation of these algorithms to minimization of extended-real-valued prox-regular functions, while covering in this way problems of constrained optimization, by using Moreau envelopes. Employing advanced techniques of second-order variational analysis and characterizations of tilt stability allows us to establish the solvability of subproblems in both algorithms and to prove the $Q$-superlinear convergence of their iterations.

中文翻译：

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非平稳优化中倾斜稳定极小化器的广义牛顿算法

SIAM优化杂志，第31卷，第2期，第1184-1214页，2021年1月。
本文旨在开发两种版本的广义牛顿法，以计算局部极小值，以解决满足约束重要稳定性（称为倾斜稳定性）的无约束和约束优化的非光滑问题。我们从具有Lipschitzian梯度的连续可分成本函数的无约束最小化开始，并提出两种牛顿类型的二阶算法：一种涉及Lipschitzian梯度映射的代码导数，另一种基于后者的图形导数。然后，我们进行这些算法的传播，以最小化扩展的实值近似正则规则函数，同时通过使用Moreau包络以这种方式涵盖约束优化的问题。