Iterative Methods for Triple Hierarchical Variational Inequalities in Hilbert Spaces

作者：Ceng, Lu-Chuan; Ansari, Qamrul Hasan^*; Yao, Jen-Chih

来源：Journal of Optimization Theory and Applications, 2011, 151(3): 489-512.

DOI：10.1007/s10957-011-9882-7

• Triple hierarchical variational inequalities
• Iterative methods
• Implicit schemes
• Explicit schemes
• Fixed points
• Nonexpansive mappings

In this paper, we consider a variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping called triple hierarchical variational inequality. We propose two iterative methods, one is implicit and another one is explicit, to compute the approximate solutions of our problem. We present an example of our problem. The convergence analysis of the sequences generated by the proposed methods is also studied.

• 单位
  上海大学; 上海师范大学