求解非光滑广义方程的修正牛顿-秒法

IF 1.6 3区数学 Q1 MATHEMATICS Mathematical Modelling and Analysis Pub Date : 2024-03-26 DOI:10.3846/mma.2024.18680

Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza

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引用次数: 0

摘要

在本文中，我们通过假设赫尔德条件，使用改进的牛顿-秒方法研究了巴拿赫空间中的非光滑广义方程的可解性。同时，我们对 Dennis-Moré 定理进行了概括，以描述所提方法在强度量次规则性条件下对非光滑广义方程的超线性收敛性。我们还提供了数值示例来说明我们方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A MODIFIED NEWTON-SECANT METHOD FOR SOLVING NONSMOOTH GENERALIZED EQUATIONS

In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.

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