In this paper, we consider a triple hierarchical variational inequality defined over the common solution set of minimization and mixed equilibrium problems. Combining the hybrid steepest-descent method, viscosity approximation method and averaged mapping approach to the gradient-projection algorithm, we propose two iterative methods: implicit one and explicit one, to compute the approximate solutions of our problem. The convergence analysis of the sequences generated by the proposed methods is also established.
"HYBRID STEEPEST-DESCENT METHODS FOR TRIPLE HIERARCHICAL VARIATIONAL INEQUALITIES." Taiwanese J. Math. 17 (4) 1441 - 1472, 2013. https://doi.org/10.11650/tjm.17.2013.2864