Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints

In this paper, we introduce and analyze a multi-step hybrid steepest-descent algorithm by combining Ko-rpelevich’s extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann’s iteration method and gradient-projection method (GPM) with regularization in the setting of infinite-dimensional Hilbert spaces. Strong convergence was established.