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A Relaxed Projection Method for Split Variational Inequalities

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  • Hongjin He

    (Hangzhou Dianzi University)

  • Chen Ling

    (Hangzhou Dianzi University)

  • Hong-Kun Xu

    (National Sun Yat-sen University)

Abstract

We study the recently introduced split variational inequality under the framework of variational inequalities in a product space. The feature of our equivalent formulation of split variational inequality is its variable separability (that is, splitting nature) together with a linear constraint. We propose a relaxed projection method, which fully exploits the splitting structure of split variational inequality and which is not only easily implementable, but also globally convergent under some mild conditions. Our numerical results on finding the minimum-norm solution of the split feasibility problem and on solving a separable and convex quadratic programming problem verify the efficiency and stability of our new method.

Suggested Citation

  • Hongjin He & Chen Ling & Hong-Kun Xu, 2015. "A Relaxed Projection Method for Split Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 213-233, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0598-3
    DOI: 10.1007/s10957-014-0598-3
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    References listed on IDEAS

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    1. D. Han, 2007. "Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 227-243, February.
    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. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    4. Bing-Sheng He, 2009. "Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities," Computational Optimization and Applications, Springer, vol. 42(2), pages 195-212, March.
    5. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
    6. Min Tao & Xiaoming Yuan, 2012. "An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures," Computational Optimization and Applications, Springer, vol. 52(2), pages 439-461, June.
    7. 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.
    8. M. H. Xu, 2007. "Proximal Alternating Directions Method for Structured Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 107-117, July.
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