New hybrid projection method and shrinking projection method for solving the multiple-set split variational inequality problem in Hilbert spaces
Date:
Abstract: In this talk, we study the multiple-set split variational inequality problem with monotone and Lipschitz continuous operators in real Hilbert spaces. Our new algorithms for solving this problem are based on the calculation of the metric projection onto the intersection of finite convex sets. To be more specific, we propose two new algorithms combining the proximal point algorithm with the hybrid projection method or the shrinking projection method. The strong convergence theorems for them are established under some feasible assumptions. Next, in some deduced cases, we obtained some results which are equivalent to the algorithms introduced by K. Nakajo and W. Takahashi (J. Math. Anal. Appl., 279, 372–379, 2003) and W. Takahashi (J. Math. Anal. Appl., 341(1), 276–286, 2008). Some numerical examples are also given to illustrate the convergence analysis of the proposed methods.