Continuation Methods for the Nonlinear Complementarity and Variational Inequality Problems in Finite Dimensions

近年来，人们对这一领域的研究兴趣越来越大， 关于有限维变分不等式和非线性 互补性问题。 在许多适用于 在解决这些问题时，有一种特殊的算法脱颖而出， 最有前途的 这是牛顿的方法。 尽管取得了成功， 方法在实践中取得了成功，该方法本质上是一种局部的 收敛算法，在这个意义上说，除非初始值是 在接近解时，一般不能保证收敛。 它 是我们研究的目标，试图扩大的领域， 牛顿法的收敛性 该方法是基于 解非线性方程组的经典延拓思想 方程，并利用最近的一些结果的灵敏度 变分不等式/互补问题的分析

In recent years, there has been a growing amount of research interests on the finite-dimensional variational inequality and nonlinear complementarity problems. Among the many algorithms applicable for solving these problems, one particular algorithm stands out as the most promising. This is Newton's method. Despite the successes this method has achieved in practice, the method is intrinsically a locally convergent algorithm in the sense that unless the initial iterate is close to the solution, convergence is, in general, not guaranteed. It is the objective of our research to attempt to enlarge the domain of convergence of Newton's method. The approach is based on the classical idea of continuation for solving systems of nonlinear equations, and makes use of some recent results of sensitivity analysis for the variation inequality/complementarity problems.