Abstract

Numerical methods for solving multivalued variational inequalities (MVI) require that the underlying mapping is either monotone or Lipschitz continuous. The authors propose a proximal point algorithm to find x∈C and w∈F(x) by solving the auxiliary variational inequality: ⟨w+M(x−xk),y−x⟩≥0,∀y∈C, where C is closed convex subset of Rn, the mapping F(x) is not Lipschitzian and M is positive definite, but not necessarily symmetric. The proximal point algorithm is coupled with the Banach contraction method to solve the MVI. Convergence proofs are given and numerical results illustrate the performance of the method.