Hierarchical problems with applications to mathematical programming with multiple sets split feasibility constraints

Fixexd point theory and applications

Zenn-Tsun Yu¹  Lai-Jiu Lin² 

[1] 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;    multiple sets split feasibility problem;    fixed point problem;    mathematical programming;    quadratic function programming;    minimum norm solution;   

DOI  :  10.1186/1687-1812-2013-283

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints.

【 授权许可】

CC BY