关于变分与互补问题的线性逼近方法的收敛性分析(英文)

On the convergence of the linear approximation methods for variational and complementarity problems

建立了Pans与Chan提出的求解变分不等问题的线性逼近方法的Kantorovich型收敛性理论．对于其特殊情形Newton法，刻划了其收敛速度及误差估计，给出了关于变分不等问题的新型的解的的存在唯一性条件，且为迭代序列的初始选取提供了可靠的依据．

This paper thoroughly establishes the Kantorovich-type convergence theories for the linear approximation methods (LAMs) set up by Pang and Chan in 1982 for solving the variational inequality problems. For the important special case Newton method, the convergence rate and error estimate are particularly described in precision and detail. This work, besides giving new existence and uniqueness conditions for the solution of the variational inequality problem, also affords reliable principles for the choices of the starting vectors of the iterations.