变分不等式和非扩张映射的迭代收敛性

Iterative convergence of variational inequalities and non-expansive mappings

介绍了一类包含非扩张映射的变分不等式和Wiener-Hopf方程,基于投影技巧推导出两者之间的等价关系,利用该等价关系提出了一个同步求解非扩张映射不动点和变分不等式的迭代算法,并在适当条件下证明了该迭代算法的强收敛性;所得结论推广了该领域内的一些最新结果.

A class of variational inequalities including non-expansive mappings and Wiener-Hopf equation are introduced, based on projection technique, the equivalence relation between the two is deduced. On the basis of this equivalence relation, an iterative algorithm for synchronously solving non-expansive mappings＇fixed points and variational inequalities is proposed. Under the proper condition, the strong convergence of this iterative algorithm is proven, and the corresponding conclusions generalize some new results in this field.