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An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space
This paper is concerned with the variational inequality problem (VIP) over
the fixed point set of a quasi-nonexpansive operator. We propose, in
particular, an algorithm which entails, at each step, projecting onto a
suitably chosen half-space, and prove that the sequences it generates converge
to the unique solution of the VIP. We also present an application of our result
to a hierarchical optimization problem.Comment: Accepted for publication in Numerical Functional Analysis and
Optimizatio