# On descent-projection method for solving the split feasibility problems

## Author Info

• Abdellah Bnouhachem

()

()

• Mohamed Khalfaoui
• Sheng Zhaohan
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## 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

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File URL: http://hdl.handle.net/10.1007/s10898-011-9782-2

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## Bibliographic Info

Article provided by Springer in its journal Journal of Global Optimization.

Volume (Year): 54 (2012)
Issue (Month): 3 (November)
Pages: 627-639

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Handle: RePEc:spr:jglopt:v:54:y:2012:i:3:p:627-639

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## Related research

Keywords: Variational inequalities; Split feasibility problems; Convergence; Iterative methods; 90C33; 49J40;

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• 90C - - - - - -
• 49J - - - - - -

## References

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1. Manishi Prasad & Peter Wahlqvist & Rich Shikiar & Ya-Chen Tina Shih, 2004. "A," PharmacoEconomics, Springer Healthcare | Adis, vol. 22(4), pages 225-244.
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