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一般多值混合隐拟变分不等式的解的存在性与算法

曾六川

曾六川. 一般多值混合隐拟变分不等式的解的存在性与算法[J]. 应用数学和力学, 2003, 24(11): 1170-1178.
引用本文: 曾六川. 一般多值混合隐拟变分不等式的解的存在性与算法[J]. 应用数学和力学, 2003, 24(11): 1170-1178.
ZENG Liu-chuan. Existence and Algorithm of Solutions for General Multivalued Mixed Implicit Quasi-Variational Inequalities[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1170-1178.
Citation: ZENG Liu-chuan. Existence and Algorithm of Solutions for General Multivalued Mixed Implicit Quasi-Variational Inequalities[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1170-1178.

一般多值混合隐拟变分不等式的解的存在性与算法

基金项目: 高等学校优秀青年教师教学和科研奖励基金资助项目;上海市教委重点学科经费资助项目;上海市高等学校科学技术发展基金资助项目
详细信息
    作者简介:

    曾六川(1965- ),男,湖南人,教授,博士生导师,已发表论文70余篇(E-mail:zengle@hotmail.com).

  • 中图分类号: O177.91

Existence and Algorithm of Solutions for General Multivalued Mixed Implicit Quasi-Variational Inequalities

  • 摘要: 引入了实Hilbert空间中一类新的一般多值混合隐拟变分不等式.它概括了丁协平教授引入与研究过的熟知的广义混合隐拟变分不等式类成特例.运用辅助变分原理技巧来解这类一般多值混合隐拟变分不等式.首先,定义了具真凸下半连续的二元泛函的新的辅助变分不等式,并选取了一适当的泛函,使得其唯一的最小值点等价于此辅助变分不等式的解.其次,利用此辅助变分不等式,构造了用于计算一般多值混合隐拟变分不等式逼近解的新的迭代算法.在此,等价性保证了算法能够生成一列逼近解.最后,证明了一般多值混合隐拟变分不等式解的存在性与逼近解的收敛性.而且,给算法提供了新的收敛判据.因此,结果对M.A.Noor提出的公开问题给出了一个肯定答案,并推广和改进了关于各种变分不等式与补问题的早期与最近的结果,包括最近文献中涉及单值与集值映象的有关混合变分不等式、混合拟变不等式与拟补问题的相应结果.
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出版历程
  • 收稿日期:  2001-07-19
  • 修回日期:  2003-06-19
  • 刊出日期:  2003-11-15

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