A golden ratio proximal method for monotone variational inequality problems

In this work, we propose a golden ratio proximal algorithm for solving monotone variational inequality problems in a real Hilbert space. It is a self-adaptive technique, endowed with a conjugate gradient type direction to facilitate convergence, and requires one evaluation of the underlying operator in an iteration. We established the convergence of the proposed method under appropriate assumptions. Numerical examples demonstrate the robustness and efficiency of the proposed method compared with some state-of-the-art methods. Additionally, we present an application of the proposed algorithms in the tomography reconstruction problem.