Regularized gradient-projection methods for the constrained convex minimization problem and the zero points of maximal monotone operator

In this paper, based on the viscosity approximation method and the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the set of zero points of the maximal monotone operator problem. In particular, the set of zero...

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Veröffentlicht in:Fixed point theory and applications (Hindawi Publishing Corporation) Jg. 2015; H. 1; S. 1 - 23
Hauptverfasser: Tian, Ming, Jiao, Si-Wen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.02.2015
Schlagworte:
Algorithms
Analysis
Applications of Mathematics
Approximation
Constraints
Convergence
Differential Geometry
Feasibility
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Minimization
Operators
Optimization
Topology
maximal monotone operator
58E35
fixed point
equilibrium problem
47H09
variational inequality
iterative method
constrained convex minimization
resolvent
65J15
ISSN:1687-1812, 1687-1812
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Zusammenfassung:In this paper, based on the viscosity approximation method and the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the set of zero points of the maximal monotone operator problem. In particular, the set of zero points of the maximal monotone operator problem can be transformed into the equilibrium problem. Under suitable conditions, new strong convergence theorems are obtained, which are useful in nonlinear analysis and optimization. As an application, we apply our algorithm to solving the split feasibility problem and the constrained convex minimization problem in Hilbert spaces.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-015-0258-9