We use the concept of barrier-based smoothing approximations to extend the non-interior continuation method, which was proposed by B. Chen and N. Xiu for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions, to an inexact non-interior continuation method for variational inequalities over general closed convex sets. Newton equations involved in the method are solved inexactly to deal with high dimension problems. The method is proved to have global linear and local superlinear/quadratic convergence under suitable assumptions. We apply the method to non-negative orthants, positive semidefinite cones, polyhedral sets, epigraphs of matrix operator norm cone and epigraphs of matrix nuclear norm cone.

我们使用基于势垒的平滑近似概念将由B.Chen和N.Xiu提出的基于Chen-Mangasarian平滑函数的非线性互补问题的非内部连续方法扩展为不精确的非内部连续方法一般封闭凸集上的变分不等式。该方法涉及的牛顿方程不精确地求解，以解决高维问题。在适当的假设下，该方法被证明具有全局线性和局部超线性/二次收敛性。我们将该方法应用于非负正割线，正半定锥，多面体集，矩阵算子范数锥的题词和矩阵核范数锥的题词。