TWO NEW INERTIAL RELAXED CQ ALGORITHMS FOR A CLASS OF BILEVEL VARIATIONAL INEQUALITIES WITH THE SPLIT FEASIBILITY PROBLEM CONSTRAINTS.

In this paper, we investigate the problem of solving strongly monotone variational inequalities over the solution sets of split feasibility problems with multiple output sets in real Hilbert spaces. We present two new iterative algorithms when the involved subsets are given as the level sets of convex functions. In our algorithms, the projection to the half-space is replaced by the one to the intersection of two half-spaces. The algorithms are accelerated using the inertial technique and eliminate the need for calculating or estimating the norms of linear operators by employing self-adaptive step size criteria. We give convergence of the sequence generated by our algorithms under some suitable assumptions. Some applications to monotone variational inequalities over the solution set of the split feasibility problem are also reported. Finally, we present some numerical examples to illustrate the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature. [ABSTRACT FROM AUTHOR]