Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem
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Authors
Ming Tian
- College of Since, Civil Aviation University of China, Tianjin 300300, China.
- Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China.
Hui-Fang Zhang
- College of Since, Civil Aviation University of China, Tianjin 300300, China.
Abstract
The gradient-projection algorithm (GPA) is an effective method for solving the constrained convex
minimization problem. Ordinarily, under some conditions, the minimization problem has more than one
solution, so the regulation is used to find the minimum-norm solution of the minimization problem. In
this article, we come up with a regularized gradient-projection algorithm to find a common element of the
solution set of equilibrium and the solution set of the constrained convex minimization problem, which is
the minimum-norm solution of equilibrium and the constrained convex minimization problem. Under some
suitable conditions, we can obtain some strong convergence theorems. As an application, we apply our
algorithm to solve the split feasibility problem and the constrained convex minimization problem in Hilbert
spaces.
Share and Cite
ISRP Style
Ming Tian, Hui-Fang Zhang, Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 9, 5316--5331
AMA Style
Tian Ming, Zhang Hui-Fang, Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem. J. Nonlinear Sci. Appl. (2016); 9(9):5316--5331
Chicago/Turabian Style
Tian, Ming, Zhang, Hui-Fang. "Regularized gradient-projection methods for finding the minimum-norm solution of equilibrium and the constrained convex minimization problem." Journal of Nonlinear Sciences and Applications, 9, no. 9 (2016): 5316--5331
Keywords
- Iterative method
- equilibrium problem
- constrained convex minimization problem
- variational inequality
- regularization
- minimum-norm.
MSC
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