解变分不等式与不动点问题的一种修正的惯性投影算法

doi:10.6040/j.issn.1671-9352.0.2022.431

摘要/Abstract

摘要： 提出了一种修正的惯性投影算法,用以寻找伪单调变分不等式问题的解集与带有半压缩映射的不动点集的公共元,在Lipschitz连续及自适应步长的条件下,证明了由该算法所产生的迭代序列强收敛于某公共元。最后,用数值实验验证了该算法的有效性。

关键词: 伪单调变分不等式, 不动点, 惯性收缩投影算法, 半压缩映射, 强收敛

Abstract: A modified inertial projection algorithm is proposed to find the common element of the set of pseudomonotone variational inequality problems and the fixed point set with a demicontractive mapping, and it is proved that the iterative sequence generated by the algorithm is strongly converged on a common element under the condition that the algorithm is implemented with a self-adaptive step size rule and the Lipschitz continuity. Finally, we implement some computational tests to show the efficiency and advantages of the proposed method.

Key words: pseudomonotone variational inequality, fixed point, inertial projection and contraction method, demicontractive mapping, strong convergence

中图分类号:

O178

陈晶晶,杨延涛. 解变分不等式与不动点问题的一种修正的惯性投影算法[J]. 《山东大学学报(理学版)》, 2023, 58(3): 64-76.

CHEN Jing-jing, YANG Yan-tao. Modified inertial projection algorithm for solving variational inequality and fixed point problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(3): 64-76.

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