Strong convergence of relaxed hybrid steepest-descent methods for triple hierarchical constrained optimization

Fixexd point theory and applications

J C Yao¹  M M Wong²  L C Zeng³ 

[1] Center for General Education, Kaohsiung Medical University, Kaohsiung, Taiwan;Department of Applied Mathematics, Chung Yuan Christian University, Chung Li, Taiwan;Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China

关键词: triple-hierarchical constrained optimization;    variational inequality;    monotone operator;    relaxed hybrid steepest-descent method;    nonexpansive mapping;    fixed point;    strong convergence;   

DOI  :  10.1186/1687-1812-2012-29

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Up to now, a large number of practical problems such as signal processing and network resource allocation have been formulated as the monotone variational inequality over the fixed point set of a nonexpansive mapping, and iterative algorithms for solving these problems have been proposed. The purpose of this article is to investigate a monotone variational inequality with variational inequality constraint over the fixed point set of one or finitely many nonexpansive mappings, which is called the triple-hierarchical constrained optimization. Two relaxed hybrid steepest-descent algorithms for solving the triple-hierarchical constrained optimization are proposed. Strong convergence for them is proven. Applications of these results to constrained generalized pseudoinverse are included. AMS Subject Classifications: 49J40; 65K05; 47H09.

【 授权许可】

CC BY