On descent-projection method for solving the split feasibility problems

Abdellah Bnouhachem (), Muhammad Noor (), Mohamed Khalfaoui and Sheng Zhaohan

Journal of Global Optimization, 2012, vol. 54, issue 3, 627-639

Abstract: Let Ω 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. Copyright Springer Science+Business Media, LLC. 2012

Keywords: Variational inequalities; Split feasibility problems; Convergence; Iterative methods; 90C33; 49J40 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-011-9782-2

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