A new hybrid projection - proximal point algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces
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Abstract: In this talk, we study the multiple-set split variational inequality problem in Hilbert spaces. Before presenting the new algorithm, we talk about a way for the implementation of hybrid projection method, in which we compute the projection of a given point onto the intersection of a finite system of closed convex sets in some special cases. Then, we propose a new algorithm combining the hybrid projection method with the proximal point algorithm, and establish a strong convergence theorem for it. Some applications of our main results regarding the solution of the split variational inequality problem and the multiple-set split feasibility problem are presented and show that the iterative method converges strongly under weaker assumptions than the ones used recently by Anh (J. Fixed Point Theory Appl. 19:2681–2696, 2017), Buong (Numer. Algorithms, 76:783–798, 2017) and Xu (Inverse Problems, 22:2021– 2034, 2006). Some numerical examples are also given to illustrate the convergence analysis of the considered method.