论文标题
非平滑优化的倾斜稳定最小化器的牛顿算法广义
Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
论文作者
论文摘要
本文旨在开发两种广义牛顿方法的版本，不仅计算非平滑优化问题的任意局部最小化器，而且只是具有重要稳定性属性质量稳定性的重要稳定性。我们从具有Lipschitzian梯度的连续微分成本函数的不受限制最小化开始，并提出了牛顿类型的两种二阶算法：一种涉及Lipschitzian梯度映射的代码，另一个基于后者的图形衍生物。然后，我们将这些算法传播以最大程度地限制扩展的实现的代表函数，同时使用Moreau信封以这种约束优化的问题覆盖。采用二阶变分析的先进技术和倾斜稳定性的特征，使我们能够在算法中建立子问题的可溶性，并证明其迭代的Q-superlineareareareareareareare。
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess 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 the 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 envelops. 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.
