A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-17
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The constrained convex minimization problem is to find a point x∗ with the property that x∗∈C, and h(x∗)=min h(x), ∀x∈C, where C is a nonempty, closed, and convex subset of a real Hilbert space H, h(x) is a real-valued convex function, and h(x) is not Fréchet differentiable, but lower semicontinuous.
In this paper, we discuss an iterative algorithm which is different from traditional gradient-projection algorithms.
We firstly construct a bifunction F1(x,y) defined as F1(x,y)=h(y)−h(x).
And we ensure the equilibrium problem for F1(x,y) equivalent to the above optimization problem.
Then we use iterative methods for equilibrium problems to study the above optimization problem.
Based on Jung’s method (2011), we propose a general approximation method and prove the strong convergence of our algorithm to a solution of the above optimization problem.
In addition, we apply the proposed iterative algorithm for finding a solution of the split feasibility problem and establish the strong convergence theorem.
The results of this paper extend and improve some existing results.
American Psychological Association (APA)
Tian, Ming& Huang, Li-Hua. 2014. A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-450235
Modern Language Association (MLA)
Tian, Ming& Huang, Li-Hua. A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces. Journal of Applied Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-450235
American Medical Association (AMA)
Tian, Ming& Huang, Li-Hua. A General Approximation Method for a Kind of Convex Optimization Problems in Hilbert Spaces. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-450235
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450235