求解非lipschitzian伪单调变分不等式的一种新的自适应步长提取法

IF 1.4 4区数学 Q1 MATHEMATICS

Carpathian Journal of Mathematics Pub Date : 2022-02-28 DOI:10.37193/cjm.2022.02.19

Duong Viet Thong

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引用次数: 0

摘要

“本工作的目的是发展一种新的外梯度方法来求解实Hilbert空间中的非Lipschitz和伪单调变分不等式。首先，我们证明了所提出的算法在松弛假设下弱收敛的一个充分条件。其次，在强伪单调性和Lipschitz-连续性假设下，我们还得到了一个Q线性凸算子该算法的收敛率。我们的结果改进了文献中关于超梯度方法的一些最新贡献。“

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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"Extragradient method with a new adaptive step size for solving non-Lipschitzian pseudo-monotone variational inequalities"

"The purpose of this work is to develop a new version of the extragradient method for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. First, we prove a sufficient condition for weak convergence of a proposed algorithm under relaxed assumptions. Next, under strong pseudomonotonicity and Lipschitz continuity assumptions, we obtain also a Q-linear convergence rate of this algorithm. Our results improve some recent contributions in the literature on the extragradient method."

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来源期刊

Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.