On Maingé's approach for hierarchical optimization problems (Q1762410)

This paper deals with an iterative method for solving a system of variational inequalities with fixed-point set constraints. Inspired by the iterative scheme for hierarchical optimization problems proposed by Maingé, the authors establish a more general variant of his scheme to obtain a strong convergence theorem on Hilbert space settings. With this new technique, the range of some parameters as it was the case in Maingé's result is relaxed. As a complementary result, the authors show how to adapt these processes to the case when the constraints involve operators belonging to the class of hemi-contractive mappings which is beyond the scope of Maingé's result.