On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method

Taksaporn Sirirut and Pattanapong Tianchai

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-10

Abstract:

Let and be closed convex subsets of real Hilbert spaces and , respectively, and let be a strictly real-valued convex function such that the gradient is an -ism with a constant . 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 of the function over set . As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find such that where 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1580837

DOI: 10.1155/2018/1580837

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