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Paper   IPM / M / 17311
School of Mathematics
  Title:   Variational inequality problem over the solution set of split monotone variational inclusion problem with application to bilevel programming problem
  Author(s):  Mohammad Eslamian
  Status:   Published
  Journal: Filomat
  Vol.:  37
  Year:  2023
  Pages:   8361-8376
  Supported by:  IPM
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.

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