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A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs

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  • Sun, Jie
  • Zhang, Su

Abstract

We propose a modified alternating direction method for solving convex quadratically constrained quadratic semidefinite optimization problems. The method is a first-order method, therefore requires much less computational effort per iteration than the second-order approaches such as the interior point methods or the smoothing Newton methods. In fact, only a single inexact metric projection onto the positive semidefinite cone is required at each iteration. We prove global convergence and provide numerical evidence to show the effectiveness of this method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1210-1220
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    References listed on IDEAS

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    1. Jia-Wang Nie & Ya-Xiang Yuan, 2001. "A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps," Annals of Operations Research, Springer, vol. 103(1), pages 115-133, March.
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    Cited by:

    1. 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.
    2. 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.
    3. Xingcai Zhou & Yu Xiang, 2022. "ADMM-Based Differential Privacy Learning for Penalized Quantile Regression on Distributed Functional Data," Mathematics, MDPI, vol. 10(16), pages 1-28, August.
    4. Deren Han & Xiaoming Yuan & Wenxing Zhang & Xingju Cai, 2013. "An ADM-based splitting method for separable convex programming," Computational Optimization and Applications, Springer, vol. 54(2), pages 343-369, March.
    5. K. Wang & D. R. Han & L. L. Xu, 2013. "A Parallel Splitting Method for Separable Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 138-158, October.
    6. Huiling Lin, 2012. "An inexact spectral bundle method for convex quadratic semidefinite programming," Computational Optimization and Applications, Springer, vol. 53(1), pages 45-89, September.
    7. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    8. 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.
    9. Bingsheng He & Min Tao & Xiaoming Yuan, 2017. "Convergence Rate Analysis for the Alternating Direction Method of Multipliers with a Substitution Procedure for Separable Convex Programming," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 662-691, August.
    10. 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.
    11. Guoyong Gu & Bingsheng He & Xiaoming Yuan, 2014. "Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 135-161, October.
    12. 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.

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