Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
复制标题
非光滑优化中倾斜稳定极小化的广义牛顿算法
DOI：
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复制
发表时间：
2020
影响因子：
3.1
通讯作者：
Ebrahim Sarabi
中科院分区：
文献类型：
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作者：
B. Mordukhovich;Ebrahim Sarabi
本文的目的是发展两个版本的广义牛顿法计算不只是任意的局部极小的非光滑优化问题，但只是那些，它具有一个重要的稳定性称为倾斜稳定性。我们从无约束最小化的连续可微成本函数具有Lipschitz梯度，并建议两个二阶牛顿型算法：一个涉及的Lipschitz梯度映射的余导数，和其他的基础上，后者的图形衍生物。然后，我们继续传播这些算法，以最小化的扩展实值的正则函数，同时以这种方式覆盖的约束优化问题，通过使用Moreau算法。采用先进的技术，二阶变分分析和倾斜稳定的特征，使我们能够建立在这两种算法的子问题的可解性，并证明其迭代的Q-超线性收敛。
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.
影响因子：
1.3
作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
通讯作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
DOI：
10.1287/moor.2020.1074
发表时间：
2019-05
期刊：
Math. Oper. Res.
影响因子：
--
作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi
通讯作者：
Ashkan Mohammadi;B. Mordukhovich;M. Sarabi