APPLICATION OF QUASI-NONEXPANSIVE OPERATORS TO AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY

作者：Cegielski Andrzej^*

来源：SIAM Journal on Optimization, 2015, 25(4): 2165-2181.

DOI：10.1137/15M1012438

• variational inequality problem
• fixed point
• quasi-nonexpansive operator
• demi-closedness principle
• approximately shrinking operator

In this paper, we prove the convergence in a norm of sequences generated by an iterative process for solving a variational inequality over the subset of fixed points of a quasi-nonexpansive operator T defined on a Hilbert space. The process employs a sequence of quasi-nonexpansive operators for which the subset of common fixed points contains FixT. We prove the convergence under a demi-closedness type condition for the sequence of operators as well as under the assumption that the process is approximately shrinking. We also give examples of methods satisfying these assumptions.

• 出版日期2015