A Tseng algorithm based on the golden ratio technique for solving variational inequality problems in Hilbert spaces.

Abstract This study is concerned with an iterative approximation of solution to variational inequality problem. We propose a Tseng iterative method based on the golden ratio technique for solving the variational inequality problem associated with a quasimonotone operator in Hilbert spaces. The propose method is self adaptive which implies the need to know the Lipschitz condition of the cost operator does not arise. Under some suitable and standard assumptions on the control parameters and the cost operator we prove that the sequence of iterate generated by the method converge weakly to a point in the solution set of the problem. Also, when the operator is assumed to be strongly pseudomonotone, we establish a R-linear convergence of the method. Finally, we report some numerical experiment to illustrate the performance of the proposed method.