混合变分不等式的一类迭代算法

Some Iterative Algorithms for Mixed Variational Inequalities

提出求解混合变分不等式的一个新的迭代算法1,并且当f是非空闭凸集K上的指示函数时,得到求解经典变分不等式的迭代算法2.对于算法1,在假设混合变分不等式的解集非空及不需要lim/(n→∞)βn=0的条件下,证明迭代序列{un}收敛于混变分不等式的唯一解.

A new iterative algorithm 1 for solving mixed variational inequalities is proposed,and when f is the indicator function over a closed convex set K,we obtain algorithm 2 for solving classical variational inequalities. For algorithm 1 where limn→∞βn=0 is removed, suppose the solution set is noempty. That the iterative sequeuce {un} converges to the unique solution of mixed variational inequalities is proved.