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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| Vydáno v: | Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2015; číslo 1; s. 1 - 23 |
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| Jazyk: | angličtina |
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01.02.2015
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 11 |
| Author | Tian, Ming Jiao, Si-Wen |
| Author_xml | – sequence: 1 givenname: Ming surname: Tian fullname: Tian, Ming email: tianming1963@126.com organization: College of Science, Civil Aviation University of China, Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China – sequence: 2 givenname: Si-Wen surname: Jiao fullname: Jiao, Si-Wen organization: College of Science, Civil Aviation University of China |
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| Title | Regularized gradient-projection methods for the constrained convex minimization problem and the zero points of maximal monotone operator |
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