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Proximal Alternating Directions Method for Structured Variational Inequalities

Author

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  • M. H. Xu

    (Nanjing University
    Jiangsu Polytechnic University)

Abstract

In the alternating directions method, the relaxation factor $\gamma\in(0,\frac{\sqrt{5}+1}{2})$ by Glowinski is useful in practical computations for structured variational inequalities. This paper points out that the same restriction region of the relaxation factor is also valid in the proximal alternating directions method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:1:d:10.1007_s10957-007-9192-2
    DOI: 10.1007/s10957-007-9192-2
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    Citations

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    Cited by:

    1. Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    2. Min Tao, 2020. "Convergence study of indefinite proximal ADMM with a relaxation factor," Computational Optimization and Applications, Springer, vol. 77(1), pages 91-123, September.
    3. M. H. Xu & T. Wu, 2011. "A Class of Linearized Proximal Alternating Direction Methods," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 321-337, November.
    4. Jiaxin Xie, 2018. "On inexact ADMMs with relative error criteria," Computational Optimization and Applications, Springer, vol. 71(3), pages 743-765, December.
    5. Cesare Molinari & Juan Peypouquet, 2018. "Lagrangian Penalization Scheme with Parallel Forward–Backward Splitting," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 413-447, May.
    6. Juan Peypouquet, 2012. "Coupling the Gradient Method with a General Exterior Penalization Scheme for Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 123-138, April.
    7. Min Tao & Xiaoming Yuan, 2018. "On Glowinski’s Open Question on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 163-196, October.
    8. Vando A. Adona & Max L. N. Gonçalves & Jefferson G. Melo, 2019. "A Partially Inexact Proximal Alternating Direction Method of Multipliers and Its Iteration-Complexity Analysis," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 640-666, August.
    9. 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.

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