New Projected Gradient Method to Solve Variational Inequality Problem

A new optimization iterative algorithm is constructed in this article, which can be used to solve variational inequality problems. We introduce a generalized sub gradient projection operator that expands the search range of each iteration of the algorithm. Combining it with adaptive parameters, the algorithm achieves faster iteration efficiency. Finally, we provide a strong convergence theorem and its proof for the new algorithm. With the conclusion of strong convergence, the new algorithm exhibits stability, determinism, and global optimality of its solutions.