求解混合似变分不等式的一个四步迭代算法

A four-step iterative method for solving mixed quasi-variational inequalities

研究了经典变分不等式的一种重要推广形式,即混合似变分不等式;利用混合似变分不等式与不动点问题和预解方程这一等价关系,提出了一个求解混合似变分不等式的四步迭代算法;证明了该算法在算子T伪单调连续的条件下收敛;结果推广和改进了先前的求解变分不等式算法.

In this paper, the author studies the mixed quasi -variational inequalites which are an important generalization of variation inequalities, uses the fixed - point problems and the resolvent equation techniques which are equivalent to the mixed quasi - variational inequalities and suggest and analyze a four - step iterative method for solving mixed quasi - variational inequalities. The resolvent iterative methods converge for pseudomonotone and continuous operator T. The results can be viewed as significant extensions and amelioration of the previously known results for variational inequalities.