Three-Step Approximation Methods from Continuous and Discrete Perspective for Quasi-Variational Inequalities
Pub Date : 2024-06-07
DOI:10.1134/s0965542524700027
引用次数: 0
Abstract
The objective of this manuscript is to study the convergence of three-step approximation methods for quasi-variational inequalities in the general case. First, we propose the three-step dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into a three-step iterative method, which we prove to converge also when it is applied to strongly-monotone quasi-variational inequalities. In addition, we show that linear convergence is guaranteed under strong-monotonicity.
从连续和离散角度看准变量不等式的三步逼近法
摘要 本文旨在研究一般情况下准变分不等式的三步近似方法的收敛性。首先，我们提出了三步动力系统，并对生成的轨迹进行了渐近分析。该系统的显式时间离散化产生了一种三步迭代法，我们证明当该方法应用于强单调准变不等式时也会收敛。此外，我们还证明，在强单调性条件下，线性收敛是有保证的。
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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