广义非凸变分不等式解的存在性和多步迭代投影算法

On Existence of Solution and Multi-Step Iterative Projection Algorithm for Generalized Nonconvex Variational Inequalities

在Hilbert空间中引入广义非凸变分不等式问题,利用变分不等式和不动点问题的等价关系,给出了求解变分不等式的多步迭代投影算法.在适当的条件下证明了该算法的收敛性.

A generalized nonconvex variational inequality problem has been introduced in a real Hilbert space with the equivalence relation of variational inequalities and fixed point problems.A multi-step iterative projection algorithm has been given for solving this variational inequalities.The convergence of the algorithm has been 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.