Newton's method for solving generalized equations: Kantorovich's and Smale's approaches
Newton's method for solving generalized equations: Kantorovich's and Smale's approaches
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DOI：
10.1016/j.jmaa.2016.02.047
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发表时间：
2016-07
影响因子：
1.3
通讯作者：
S. Adly;H. Ngai;V. V. Nguyen-V.
中科院分区：
文献类型：
--
作者：
S. Adly;H. Ngai;V. V. Nguyen-V.
本文研究了Banach空间中集值映射广义方程的Newton型解法。证明了Kantorovich型定理（局部和全局）以及牛顿序列的二次收敛性。我们还将Smale的经典（α，γ）-理论推广到广义方程。这些结果是新的，可以认为是经典非线性方程文献中许多已知结果的推广。我们的方法是基于变分分析的工具。度量正则性的概念在我们的分析中起着重要的作用。
In this paper, we study Newton-type methods for solving generalized equations involving set-valued maps in Banach spaces. Kantorovich-type theorems (both local and global versions) are proved as well as the quadratic convergence of the Newton sequence. We also extend Smale's classical (α, γ)-theory to generalized equations. These results are new and can be considered as an extension of many known ones in the literature for classical nonlinear equations. Our approach is based on tools from variational analysis. The metric regularity concept plays an important role in our analysis.