Iterative methods for triple hierarchical variational inequalities in Hilbert spaces
A variational inequality with a variational inequality constraint over a set of fixed points of a nonexpansive mapping is considered. Such a problem is called triple hierarchical variational inequality (THVI). Two iterative methods to compute approximate solutions of the problem are proposed: one is implicit and another one is explicit. This is carried out, for the first case, by combining the regularization, the hybrid steepest-descent, and the projection methods. For the second situation, a sequence via an iterative algorithm is generated, and it is proved that this sequence converges strongly to the unique solution of the THVI.
triple hierarchical variational inequalities
scientific article; zbMATH DE number 6006028
scientific article