Alarge step adaptive sub-gradient and exter-gradient projection algorithm for pseudomonotone variational inequalities

In 2020, Pham Ky Anh et al. proposed an adaptive projection algorithm (abbreviated as PDNA) in Hilbert space for solving the mapping pseudo-monotone and Lipschitz continuous. The algorithm does not need to know the Lipschitz coefficient of the map, and has a strong convergence result. It is noted that the step size of the algorithm is closely related to its convergence speed, and generally the algorithm with long strides has better convergence speed. Liu and Yang propose an adaptive algorithm for solving quasi-monotone variational inequalities (abbreviated LYA) with a step size longer than the step size in PDNA. In this paper, we propose an adaptive subgradient external gradient projection algorithm for solving the mapping pseudo-monotone and Lipschitz continuous. The step size of the new algorithm is longer than that of LYA and can be degraded to the step size of LYA. The strong convergence of the new algorithm is proved under the same assumptions as that of PDNA. Numerical experiments show that the new algorithm has better numerical experimental results.