On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method
Joint Authors
Sirirut, Taksaporn
Tianchai, Pattanapong
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-01
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Let C and Q be closed convex subsets of real Hilbert spaces H1 and H2, respectively, and let g:C→R be a strictly real-valued convex function such that the gradient ∇g is an 1/L-ism with a constant L>0.
In this paper, we introduce an iterative scheme using the gradient projection method, based on Mann’s type approximation scheme for solving the constrained convex minimization problem (CCMP), that is, to find a minimizer q∈C of the function g over set C.
As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find q∈C such that Aq∈Q where A:H1→H2 is a linear bounded operator.
We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the CCMP and the SFP are obtained.
The results presented in this paper improve and extend the main results of Tian and Zhang (2017) and many others.
The data availability for the proposed SFP is shown and the example of this problem is also shown through numerical results.
American Psychological Association (APA)
Sirirut, Taksaporn& Tianchai, Pattanapong. 2018. On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method. International Journal of Mathematics and Mathematical Sciences،Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1173440
Modern Language Association (MLA)
Sirirut, Taksaporn& Tianchai, Pattanapong. On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method. International Journal of Mathematics and Mathematical Sciences No. 2018 (2018), pp.1-10.
https://search.emarefa.net/detail/BIM-1173440
American Medical Association (AMA)
Sirirut, Taksaporn& Tianchai, Pattanapong. On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method. International Journal of Mathematics and Mathematical Sciences. 2018. Vol. 2018, no. 2018, pp.1-10.
https://search.emarefa.net/detail/BIM-1173440
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1173440