A hybrid Josephy — Newton method for solving box constrained variational equality roblems via the D-gap function

Abstract

A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Some basic properties of the affine variational inequality subproblems in the classical Josephy—Newton method are studied. A hybrid Josephy—Newton method is then proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.