仿射变换内点信赖域方法求解变分不等式问题

摘要

本文研究了求解非线性约束变分不等式问题(VIP)的一个新的算法.利用KKT条件的非光滑方程形式,得到了与VIP等价的简单约束优化问题.提出了求解VIP的一类结合回代线搜索技巧的仿射变换内点信赖域算法.在较弱的条件下证明了算法具有整体收敛性,进一步在某些正则条件下,证明了算法具有超线性收敛速度.%In this article,we study a new algorithm for solving variational inequality problems (VIP) with nonlinear constraints.By using a nonsmooth equation reformulation of the KKT conditions,we analyze an equivalent simply constrained optimization problem of VIP and propose an affine scaling interior trust region method in association with backtracking line search technique for solving VIP.Theoretical analysis are given which prove that the proposed algorithm is globally convergent under mild conditions and further has a local superlinear convergence rate under a certain regularity condition.