Projection and contraction methods for constrained convex minimization problem and the zero points of maximal monotone operator
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Authors
Yujing Wu
- Tianjin Vocational Institute, Tianjin, 300410, P. R. China.
Luoyi Shi
- Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China.
Abstract
In this paper, we introduce a new iterative scheme for the constrained convex minimization problem and the set of zero
points of the maximal monotone operator problem, based on the projection and contraction methods. The core idea is to build
the corresponding iterative algorithms by constructing reasonable error metric function and profitable direction to assure that
the distance form the iteration points generated by the algorithms to a point of the solution set is strictly monotone decreasing.
Under suitable conditions, new convergence theorems are obtained, which are useful in nonlinear analysis and optimization.
The main advantages of the method presented are its simplicity, robustness, and ability to handle large problems with any
start point. As an application, we apply our algorithm to solve the equilibrium problem, the constrained convex minimization
problem and the split feasibility problem, the split equality problem in Hilbert spaces.
Share and Cite
ISRP Style
Yujing Wu, Luoyi Shi, Projection and contraction methods for constrained convex minimization problem and the zero points of maximal monotone operator, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 637--646
AMA Style
Wu Yujing, Shi Luoyi, Projection and contraction methods for constrained convex minimization problem and the zero points of maximal monotone operator. J. Nonlinear Sci. Appl. (2017); 10(2):637--646
Chicago/Turabian Style
Wu, Yujing, Shi, Luoyi. "Projection and contraction methods for constrained convex minimization problem and the zero points of maximal monotone operator." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 637--646
Keywords
- Fixed point
- constrained convex minimization
- maximal monotone operator
- resolvent
- variational inequality
- split equality problem.
MSC
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