Halpern projection methods for solving pseudomonotone multivalued variational inequalities in Hilbert spaces (Q2021774)

2104This paper proposes two new projection algorithms for solving multivalued variational inequalities in real Hilbert spaces. They proved that the proposed algorithms are strongly convergent under the assumption of the pseudomonotonicity and Lipschitz continuity of cost mappings. The main advantage of the proposed algorithms is that the metric projections onto the feasible set used in the current algorithms at each iteration are replaced by approximate projection or proximal operators. Finally, they provide a new and interesting example for the multivalued cost mapping and show its pseudomonotone and Lipschitz continuous properties. They perform some numerical experiments to illustrate the behavior of the proposed algorithms.