Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem

Abstract

The purpose of this paper is to study variational inequality problem over the solution set of multiple-set split monotone variational inclusion problem.
We propose  an iterative algorithm with inertial extrapolation step
for finding an approximate solution of this problem in real Hilbert spaces.
Strong convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions.The iterative
scheme does not require prior knowledge of operator norm. Also we
present some applications of our main result to solve the bilevel programming problem, the bilevel monotone variational inequalities,
the split minimization problem, the multiple-set split feasibility problem and the multiple set split variational inequality problem.