A simple fork algorithm for solving pseudomonotone non-Lipschitz variational inequalities

Low Computational Cost Algorithms for Solving Variational Inequalities over the Fixed Point Set

“…Under the assumptions that 𝐴𝐴 is 𝛾𝛾-strongly pseudomonotone and 𝐿𝐿-Lipschitz continuous on, 𝜆𝜆 ∈ (0, 2 𝛾𝛾 𝐿𝐿 2 ), the sequence {𝑥𝑥 𝑘𝑘 } generated by (2) converges linearly to the unique solution of the problem (1). If 𝐴𝐴 is only monotone instead of being strongly pseudomonotone, the Gradient projection algorithm, in general, is not convergent.…”

“…(3) Under the conditions that 𝐴𝐴 is pseudomonotone and 𝐿𝐿-Lipschitz continuous on, 𝜆𝜆 ∈ (0, 1 𝐿𝐿 ), algorithm (3) converges to a solution of (1). This algorithm has been investigated and developed by a lot of authors, see [2,3]. However, it has two drawbacks: First, it requires to compute the projection onto 𝐶𝐶 twice in each iteration.…”