数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 633-643.

• 论文 •    下一篇

广义混合变分不等式的Levitin-Polyak适定性

朱莉|夏福全   

  1. 四川师范大学数学与软件科学学院 成都 610066
  • 收稿日期:2010-05-08 修回日期:2011-10-29 出版日期:2012-08-25 发布日期:2012-08-25
  • 基金资助:

    国家自然科学基金(10671135)和四川省科技厅应用基础项目(2010JY0121)资助

Levitin-Polyak Well-posedness of Generalized Mixed Variational Inequalities

 ZHU Li, XIA Fu-Quan   

  1. Department of Mathematics, Sichuan Normal University, Chengdu |610066
  • Received:2010-05-08 Revised:2011-10-29 Online:2012-08-25 Published:2012-08-25
  • Supported by:

    国家自然科学基金(10671135)和四川省科技厅应用基础项目(2010JY0121)资助

摘要:

首先给出广义混合变分不等式的Levitin-Polyak-α -近似序列以及适定性的定义. 然后, 定义广义混合变分不等式的gap函数并证明广义混合变分不等式的Levitin-Polyak适定性与其相应的gap函数的极小化问题的Levitin-Polyak适定性之间的等价性. 最后, 研究广义混合变分不等式的(广义) Levitin-Polyak-α -适定性的Furi-Vignoli型度量性质.

关键词: Levitin-Polyak-α -适定性, 广义混合变分不等式, gap函数, 极小化问题

Abstract:

In this paper, we introduce the concepts of the Levitin-Polyak-α-approximating sequences and the  Levitin-Polyak-α-well-posedness to the generalized mixed variational inequalities. We also define the gap function of the generalized mixed variational inequalities and prove that the Levitin-Polyak well-posedness to the generalized mixed variational inequalities and the corresponding minimization problems are equivalent. After that, we investigate the Furi-Vignoli type metric characteristics of (generalized) Levitin-Polyak well-posedness to the generalized mixed variational inequalities.

Key words: Levitin-Polyak-α-well-posedness, The generalized mixed variational inequalities, Gap function, Minimization problems

中图分类号: 

  • 49J40