Viscosity method for hierarchical fixed point and variational inequalities with applications

Shi Sheng Zhang; Xiong Rui Wang; Heung Wing Joseph Lee; Chi Kin Chan

doi:10.1007/s10483-011-1410-8

Viscosity method for hierarchical fixed point and variational inequalities with applications

Shi Sheng Zhang, Xiong Rui Wang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publication › Journal article › Academic research › peer-review

9 Citations (Scopus)

Abstract

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.

Original language	English
Pages (from-to)	241-250
Number of pages	10
Journal	Applied Mathematics and Mechanics (English Edition)
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s10483-011-1410-8
Publication status	Published - 1 Feb 2011

Keywords

fixed point
hierarchical fixed point
hierarchical minimization
non-expansive mapping
viscosity approximation

ASJC Scopus subject areas

Applied Mathematics
Mechanics of Materials
Mechanical Engineering

More information

10.1007/s10483-011-1410-8

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AU - Lee, Heung Wing Joseph

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N2 - A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.

AB - A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.

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KW - hierarchical fixed point

KW - hierarchical minimization

KW - non-expansive mapping

KW - viscosity approximation

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DO - 10.1007/s10483-011-1410-8

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JO - Applied Mathematics and Mechanics (English Edition)

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ER -

Viscosity method for hierarchical fixed point and variational inequalities with applications

Abstract

Keywords

ASJC Scopus subject areas

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