Double inertial extragradient algorithms for solving variational inequality problems with convergence analysis

In this paper, we introduce a novel dual inertial Tseng's extragradient method for solving variational inequality problems in real Hilbert spaces, particularly those involving pseudomonotone and Lipschitz continuous operators. Our secondary method incorporates variable step-size, updated at each iteration based on some previous iterates. A notable advantage of these algorithms is their ability to operate without prior knowledge of Lipschitz-type constants and without the need for any line-search procedure. We establish the convergence theorem of the proposed algorithms under mild assumptions. To illustrate the numerical behavior of the algorithms and to make comparisons with other methods, we conduct several numerical experiments. The results of these evaluations are showcased and thoroughly examined to exemplify the practical significance and effectiveness of the proposed methods.