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

近年来，关于有限维变分不等式和非线性互补问题的研究越来越受到人们的关注。在许多适用于解决这些问题的算法中，有一种特别的算法是最有前途的。这就是牛顿的方法。尽管这种方法在实践中取得了成功，但该方法本质上是一个局部收敛的算法，因为除非初始迭代接近解，否则通常不能保证收敛。扩大牛顿法的收敛范围是我们研究的目标。该方法基于求解非线性方程组的经典延拓思想，并利用最近对变分不等/互补问题的灵敏度分析的一些结果。

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.