Double inertial steps with single projection method for variational inequalities involving pseudomonotone and non-Lipschitz mappings
Thong Duong Viet, Dung Vu Tien, Huyen Pham Thi Huong, Tam Hoang Thi Thanh · Research Square · 2022
Abstract In this work, we investigate pseudomonotone and non-Lipschitz continuous variational inequality in real Hilbert spaces and introduce a projection-type method with double inertial terms for solving them. The proposed algorithm combines the techniques of double inertial steps and the projection and contraction method. One only projection in the algorithm is used per iteration and the proposed algorithm does not require Lipschitz continuous condition of the variational inequality mapping and a sufficient condition for the weak convergence is established under pseudomonotonicity and uniform continuity assumptions. Next, we also obtain an R-linear convergence rate of the proposed method under strong pseudomonotonicity and Lipschitz continuity assumptions. Finally, In order to illustrate the computational effectiveness of our algorithm, some numerical results are also provided. The main results obtained in this paper extend and improve some related works in the literature.