Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces
Guo-ji Tang, Zhongping Wan, Nan‐jing Huang · Numerical Functional Analysis and Optimization · 2018
In this article, a projection-type method for mixed variational inequalities is proposed in Hilbert spaces. The proposed method has the following nice features: (i) The algorithm is well defined whether the solution set of the problem is nonempty or not, under some mild assumptions; (ii) If the solution set is nonempty, then the sequence generated by the method is strongly convergent to the solution, which is closest to the initial point; (iii) The existence of the solutions to variational inequalities can be verified through the behavior of the generated sequence. The results presented in this article generalize and improve some known results.