Inertial-type incremental constraint projection method for solving variational inequalities without Lipschitz continuity

In this paper, we propose an incremental constraint projection method (i.e., random or cyclic projection algorithm) for solving variational inequality problem with special structure, which the underlying mapping is strongly monotone and the constraint set is the intersection of a large number of simple closed convex sets. Compared with some existing projection type algorithms, the proposed method has two notable advantages: Its global convergence can be guaranteed without the Lischitz continuity of underlying mapping in almost sure sense; It just computes only one halfspace projection rather than the projection of the full or single constraint set at each iteration. Preliminary computational experience is also reported to illustrate the effectiveness of the proposed method.