Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems

Yuning Yang (), Qingzhi Yang () and Su Zhang ()
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Yuning Yang: Nankai University
Qingzhi Yang: Nankai University
Su Zhang: Nankai University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 1, No 6, 130-147

Abstract: Abstract In this paper, we propose two new multiple-sets split feasibility problem models and new solution methods. The first model is more separable than the original one, which enables us to apply a modified alternating direction method with parallel steps to solve it. Then, to overcome the difficulty of computing projections onto the constraint sets, a special version of this modified method with the strategy of projection onto half-space is given. The second model consists in finding a least Euclidean norm solution of the multiple-sets split feasibility problem, for which we provide another modified alternating direction method. Numerical results presented at the last show the efficiency of our methods.

Keywords: Multiple-sets split feasibility problem; Alternating direction method; Parallel computing; Half-space projection (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0502-6

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