An approximate bundle-type auxiliary problem method for solving generalized variational inequalities

By combining the bundle idea with the auxiliary problem method we present an algorithm for solving a generalized variational inequality problem (GVIP). The proposed algorithm only requires the approximate function values and the approximate subgradients of the involved function instead of the exact ones at some points, which makes the algorithm easier to implement. In addition to that, the conditions imposed on the auxiliary functions are weaker than the preexisting results: convex is enough, not necessarily strongly convex. We also prove the weak convergence of the proposed algorithm under some conditions.