On descent-projection method for solving the split feasibility problems

Authors:
Abdellah Bnouhachem;Muhammad Aslam Noor;Mohamed Khalfaoui;Sheng Zhaohan
Affiliations:
School of Management Science and Engineering, Nanjing University, Nanjing, People's Republic of China 210093 and Ibn Zohr University, ENSA, Agadir, Morocco;Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan and Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia;Ibn Zohr University, Agadir, Morocco;School of Management Science and Engineering, Nanjing University, Nanjing, People's Republic of China 210093
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

Let 驴 and C be nonempty, closed and convex sets in R n and R m respectively and A be an $${m \times n}$$ real matrix. The split feasibility problem is to find $${u \in \Omega}$$ with $${Au \in C.}$$ Many problems arising in the image reconstruction can be formulated in this form. In this paper, we propose a descent-projection method for solving the split feasibility problems. The method generates the new iterate by searching the optimal step size along the descent direction. Under certain conditions, the global convergence of the proposed method is proved. In order to demonstrate the efficiency of the proposed method, we provide some numerical results.