On projected alternating BB methods for variational inequalities

The Barzilai-Borwein (BB) step size initially proposed in the context of unconstrained optimization has become one of the most popular step choices for gradient-based methods in the optimization community. It is well-known that the powerful variational inequality can be used to characterize the first-order optimality condition of constrained optimization problems. However, a variational inequality problem is not always equivalent to a constrained optimization problem. In this paper, we follow the spirit of BB step size and propose a projection method with alternate BB step size for general variational inequalities. Although the global convergence is established under some strong conditions, a series of computational experiments on nonlinear complementarity problems, image deblurring problems and generalized Nash equilibrium problems demonstrate that the proposed almost-parameter-free projection method is more efficient than some existing state-of-the-art projection methods in the literature.

Automated summary

The paper introduces a projection method for general variational inequalities, inspired by the spirit of the BB step size. Computational experiments show that this method is more efficient than existing state-of-the-art projection methods.