scholarly journals Iterative methods for constrained convex minimization problem in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Ming Tian ◽  
Li-Hua Huang
Keyword(s):  
Iterative Methods ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Constrained Convex Minimization Problem

scholarly journals General Iterative Methods for System of Equilibrium Problems and Constrained Convex Minimization Problem in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Peichao Duan
Keyword(s):  
Iterative Methods ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Constrained Convex Minimization Problem ◽  
System Of Equilibrium Problems

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of solutions of system of equilibrium problems and a constrained convex minimization problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by Tian and Liu (2012) and many others. Furthermore, we give numerical example to demonstrate the effectiveness of our iterative scheme.

scholarly journals Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ming Tian ◽  
Jun-Ying Gong
Keyword(s):  
Minimization Problem ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Constrained Convex Minimization Problem ◽  
The Split Feasibility Problem ◽  
Implicit And Explicit

As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem.

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