Mathematical programming with multiple sets split monotone variational inclusion constraints

Fixexd point theory and applications

Chih-Sheng Chuang¹  Zenn-Tsun Yu²  Lai-Jiu Lin³ 

[1] Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan;Department of Electronic Engineering, Nan Kai University of Technology, Nantou, Taiwan;Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

关键词: hierarchical problems;    split variational inclusion problems;    fixed point problems;    mathematical programming;    minimum norm solution;   

DOI  :  10.1186/1687-1812-2014-20

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two numerical examples are given to demonstrate our results. As applications of our convergence theorem of the hierarchical problem, we study the unique solution for the following problems: mathematical programming with multiply sets split variational inclusion and fixed point set constraints; mathematical programming with multiple sets split variational inequalities and fixed point set constraints; the variational inequality problem with a system of mixed type equilibria and fixed point set constraints; the variational inequality problem with multiple sets split system of mixed type equilibria and fixed point set constraints; mathematical programming with a system of mixed type equilibria and fixed point set constraints. We give iteration processes for these types of problems and establish the strong convergence for the unique solution of these problems. For our special case, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibria problem; the minimum norm solution of the system of mixed type equilibria problem. Our results will have many applications in diverse fields of science.

【 授权许可】

CC BY