Iterative algorithms based on the viscosity approximation method for equilibrium and constrained convex minimization problem

The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on the viscosity approximation method, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solu...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2012; no. 1; pp. 1 - 17
Main Authors: Tian, Ming, Liu, Lei
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.11.2012
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Approximation
Constraints
Convergence
Differential Geometry
Iterative algorithms
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Minimization
Optimization
Topology
Viscosity
variational inequality
constrained convex minimization
iterative algorithm
equilibrium problem
ISSN:1687-1812, 1687-1820, 1687-1812, 2730-5422
Online Access:Get full text
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Summary:The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on the viscosity approximation method, we combine the GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this paper. Under suitable conditions, strong convergence theorems are obtained. MSC: 46N10, 47J20, 74G60.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1687-1812
1687-1820
1687-1812
2730-5422
DOI:10.1186/1687-1812-2012-201