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

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  • Yuning Yang

    (Nankai University)

  • Qingzhi Yang

    (Nankai University)

  • Su Zhang

    (Nankai University)

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.

Suggested Citation

  • Yuning Yang & Qingzhi Yang & Su Zhang, 2014. "Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 130-147, October.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:1:d:10.1007_s10957-013-0502-6
    DOI: 10.1007/s10957-013-0502-6
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    References listed on IDEAS

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    1. Sun, Jie & Zhang, Su, 2010. "A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1210-1220, December.
    2. Wenxing Zhang & Deren Han & Xiaoming Yuan, 2012. "An efficient simultaneous method for the constrained multiple-sets split feasibility problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 825-843, July.
    3. Deren Han & Xiaoming Yuan, 2012. "A Note on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 227-238, October.
    4. Xiaoming Yuan, 2011. "An improved proximal alternating direction method for monotone variational inequalities with separable structure," Computational Optimization and Applications, Springer, vol. 49(1), pages 17-29, May.
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