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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (4): 609-622.doi: 10.3969/j.issn.1005-3085.2024.04.002

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变分不等式问题和不动点问题的公共元的新投影算法

房萌凯,  高兴慧,  王永杰   

  1. 延安大学数学与计算机科学学院，延安 716000
  • 收稿日期:2022-12-13 接受日期:2023-04-27 出版日期:2024-08-15
  • 通讯作者: 高兴慧 E-mail: yadxgaoxinghui@163.com
  • 基金资助:
    国家自然科学基金 (61866038)；延安大学科研计划项目 (2023JBZR-012)；延安大学“十四五”中长期重大科研项目(2021ZCQ012).

A New Projection Algorithm for Common Elements of Variational Inequalities Problems and Fixed Point Problems

FANG Mengkai,  GAO Xinghui,  WANG Yongjie   

  1. College of Mathematics and Computer Science, Yan'an University, Yan'an 716000
  • Received:2022-12-13 Accepted:2023-04-27 Online:2024-08-15
  • Contact: X. Gao. E-mail address: yadxgaoxinghui@163.com
  • Supported by:
    The National Natural Science Foundation of China (61866038); the Scientific Research Project of Yan'an University (2023JBZR-012); the  Fourteenth Five-Year Plan Mid-long Term Major Research Program of Yan'an University (2021ZCQ012).

摘要： 在Hilbert空间中针对求解变分不等式问题和不动点问题的公共元给出一种新的投影算法，在适当的条件下，采用粘性逼近方法和投影算子的技巧证明了由该算法生成的迭代序列强收敛于伪单调变分不等式解集和两个半压缩映射公共不动点集的公共元。最后，给出数值实验说明该算法的有效性优于已有算法。

关键词: 变分不等式, 不动点, 投影算法, 半压缩映射

Abstract:

A new projection algorithm is proposed for the common elements of variational inequality problems and fixed point problems. Under appropriate conditions, it is proved that the iterative sequence generated by the algorithm strongly converges to the common element of the solution set for pseudomonotone variational inequality problem and the common fixed point set of two semi-contractive mappings by using viscous approximation method and projection operator skills. Finally, numerical experiments illustrate the effectiveness of the algorithm and shou that the performance of the proposed algorithm is better then existing alrorithm.

Key words: variational inequality, fixed point, projection algorithm, semi-contractive mapping

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