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Construction algorithms for a class of monotone variational inequalities

Authors:	Yonghong Yao Mihai Postolache Yeong-Cheng Liou Zhangsong Yao

Institution:	1.Department of Mathematics,Tianjin Polytechnic University,Tianjin,China;2.Faculty of Applied Sciences,University “Politehnica” of Bucharest,Bucharest,Romania;3.Department of Information Management,Cheng Shiu University,Kaohsiung,Taiwan;4.Center for General Education,Kaohsiung Medical University,Kaohsiung,Taiwan;5.School of Information Engineering,Nanjing Xiaozhuang University,Nanjing,China

Abstract:	This paper is devoted to solve the following monotone variational inequality of finding $x^\in \mathrm{Fix}(T)$ such that $$\begin{aligned} \langle Ax^,x-x^*\rangle \ge 0,\quad \forall x\in \mathrm{Fix}(T), \end{aligned}$$ where A is a monotone operator and $\mathrm{Fix}(T)$ is the set of fixed points of nonexpansive operator T. For this purpose, we construct an implicit algorithm and prove its convergence hierarchical to the solution of above monotone variational inequality.

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