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In this paper, we present a semi-proximal alternating direction method of multipliers (ADMM) for solving $3$-block separable convex minimization problems with the second block in the objective being a strongly convex function and one coupled linear equation constraint.
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B. S. He and X. M. Yuan, On the O ( 1 / n ) O(1/n) convergence rate of the Douglas-Rachford alternating direction method, SIAM Journal on Numerical Analysis, 50 (2012), pp. 700–709
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C. H. Chen, Y. Shen and Y. F. You, On the convergence analysis of the alternating direction method of multipliers with three blocks, Abstract and Applied Analysis, 2013 (2013), Article ID 183961, 7 pages
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M. Fazel, T. K. Pong, D. F. Sun and P. Tseng, Hankel matrix rank minimization with applications to system identification and realization, SIAM Journal on Matrix Analysis and Applications, 34(3) (2013), pp. 946–977
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2009
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J. Sun and S. Zhang, A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs, European Journal of Operational Research, 207 (2010), pp. 1210–1220
2010
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H. D. Qi and D. F. Sun, An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem, IMA Journal of Numerical Analysis, 31 (2011), pp. 491–511
2011
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D. R. Han and X. M. Yuan, A note on the alternating direction method of multipliers, Journal of Optimization Theory and Applications, 155(1) (2012), pp. 227–238
2012
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C. H. Chen, B. S. He, Y. Y. Ye and X. M. Yuan, The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent, Mathematical Programming, Ser. A, DOI 10.1007/s10107-014-0826-5, (2014)
2014
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2014
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2014
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