一般变分不等式的三步迭代算法

A Three-steps Iterative Algorithm for General Variational Inequalities

利用变分不等式和不动点问题的等价关系,给出了一个新的求解一般变分不等式的三步迭代算法;该算法在现有的两步迭代算法基础上,利用校正方法建立了第三步迭代公式;最后在适当条件下证明了该算法的收敛性,所得结论推广了该领域内的一些最新结果.

It is well known that the variational inequalities are equivalent to the fixed point problems. A new three-steps iterative algorithm is proposed for general variational inequalities based on the equivalence. The new algorithm includes the known two-steps iterative algorithm as special case, and modifies the iterative algorithm with the third-step iteration scheme by using the technique of updating. The convergence of the algorithm is proved under mild conditions. The results in this paper can be viewed as an improvement and extension of the previously known results for general variational inequalities.