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无单调性集值变分不等式的一种投影算法

陈园   

  1. 四川师范大学数学科学学院, 成都 610068
  • 收稿日期:2018-11-01 出版日期:2020-11-15 发布日期:2020-11-15
  • 基金资助:

    国家自然科学基金(11271274)资助.

陈园. 无单调性集值变分不等式的一种投影算法[J]. 计算数学, 2020, 42(4): 435-444.

Chen Yuan. A PROJECTION ALGORITHM FOR SOLVING MULTI-VALUED VARIATIONAL INEQUALITIES WITHOUT MONOTONICITY[J]. Mathematica Numerica Sinica, 2020, 42(4): 435-444.

A PROJECTION ALGORITHM FOR SOLVING MULTI-VALUED VARIATIONAL INEQUALITIES WITHOUT MONOTONICITY

Chen Yuan   

  1. Department of Mathematics, Sichuan Normal University, Chengdu 610068, China
  • Received:2018-11-01 Online:2020-11-15 Published:2020-11-15
本文给出了求解无单调性集值变分不等式的一个新的投影算法,该算法所产生的迭代序列在Minty变分不等式解集非空且映射满足一定的连续性条件下收敛到解.对比文献[10]中的算法,本文中的算法使用了不同的线性搜索和半空间,在计算本文所引的两个数值例子时,该算法比文献[10]中的算法所需迭代步更少.
In this paper, we propose a new projection algorithm for solving multi-valued variational inequalities without monotonicity. If the dual problem has a solution, the whole sequence converges to a solution of the variational inequality. Instead of the linesearch and hyperplane used in [10], we adopt different kinds of linesearch and halfspaces in our algorithm. The numerical experiment is also reported.

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