Two novel golden ratio algorithms for quasimonotone variational inequalities

In this article, we provide two viscosity-type golden ratio algorithms with different inertial terms for solving quasimonotone variational inequalities in real Hilbert spaces. Both of our algorithms use a new adaptive step size which is based on the golden ratio $(\sqrt{5}+1)/2$. Under some suitable conditions, we obtain strong convergence theorems of our proposed algorithms. Moreover, several numerical results are given to illustrate the efficiency and advantages of our proposed methods.