广义收敛分析中的三步投影方法及对变分不等式的应用

The Three-step Projection Method in Generalized Analysis and Its Application to Variational Inequality Problems

设H是一实Hilbert空间,首先给出了H空间中的一个变分不等式问题,由变分不等式与投影间的关系(张石生.变分不等式和相补问题理论及应用.上海:科学技术文献出版社,1991.)将变分不等式问题化为一个有关投影的问题,然后给出了在H空间中的一个带误差的三步投影方法.最后将该三步投影方法应用于求解变分不等式问题,给出了此方法在变分不等式中的应用.

Let H be a real Hilbert space. Firstly, a nonlinear variational inequality problem in H is introduced and transformed to a projection problem. Secondly, a generalized model called three-step projection method is introduced and analized. Finally, this method is applied to solving the problem. This is an application in variational inequality theory of the method.