Self-adaptive Prediction-correction Method for Constrained Linear Variational Inequality Problems

摘要

Projection-type methods are classical approaches for variational inequalities. This article presents a new self-adaptive projection type prediction-correction method for solving a class of linear variational inequalities. At each iteration, it only needs to perform some orthogonal projections onto simple convex sets and some matrix-vector multiplications. The method makes use of a new descent direction to produce the new iterate and can be also viewed as a projection-based descent method. Convergence of the proposed method is proved under certain conditions.