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Original Article

General parameterized proximal point algorithm with applications in statistical learning

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Pages 199-215 | Received 22 Mar 2017, Accepted 25 Nov 2017, Published online: 30 Jan 2018

References

  • J.C. Bai, H.C. Zhang, and J.C. Li, A parameterized proximal point algorithm for separable convex optimization, Optim. Lett. (2017). doi:doi: 10.1007/s11590-017-1195-9.
  • X.J. Cai, G.Y. Gu, B.S. He, and X.M. Yuan, A proximal point algorithm revisit on the alternating direction method of multipliers, Sci. China Math. 56 (2013), pp. 2179–2186.
  • V. Chandrasekaran, P.A. Parrilo, and A.S. Willsky, Latent variable graphical model selection via convex optimization, Ann. Stat. 40 (2012), pp. 1935–1967.
  • J. Eckstein and D.P. Bertsekas, On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program. 55 (1992), pp. 293–318.
  • J. Friedman, T. Hastie, and R. Tibshirani, Sparse inverse covariance estimation with the graphical lasso, Biostatistics 9 (2008), pp. 432–441.
  • G.Y. Gu, B.S. He, and X.M. Yuan, Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach, Comput. Optim. Appl. 59 (2014), pp. 135–161.
  • B.S. He, F. Ma, and X.M. Yuan, Convergence study on the symmetric version of ADMM with larger step sizes, SIAM J. Imaging Sci. 9 (2016), pp. 1467–1501.
  • B.S. He, M. Tao, and X.M. Yuan, A splitting method for separable convex programming, IMA J. Numer. Anal. 35 (2015), pp. 394–426.
  • B.S. He, H.K. Xu, and X.M. Yuan, On the proximal Jacobian decomposition of ALM for multiple-block separable convex minimization problems and its relationship to ADMM, J. Sci. Comput. 66 (2016), pp. 1204–1217.
  • B.S. He, X.M. Yuan, and W.X. Zhang, A customized proximal point algorithm for convex minimization with linear constraints, Comput. Optim. Appl. 56 (2013), pp. 559–572.
  • A.P. Liao, X.B. Yang, J.X. Xie, and Y. Lei, Analysis of convergence for the alternating direction method applied to joint sparse recovery, Appl. Math. Comput. 269 (2015), pp. 548–557.
  • Z.S. Liu, J.C. Li, G. Li, J.C. Bai, and X.N. Liu, A new model for sparse and low-rank matrix decomposition, J. Appl. Anal. Comput. 7 (2017), pp. 600–616.
  • S.Q. Ma, Alternating proximal gradient method for convex minimization, J. Sci. Comput. 68 (2016), pp. 546–572.
  • F. Ma and M.F. Ni, A class of customized proximal point algorithms for linearly constrained convex optimization, Comp. Appl. Math. (2016), pp. 1–6. doi:doi: 10.1007/s40314-016-0371-3.
  • B. Martinet, Regularisation, d'inéquations variationelles par approximations succesives, Rev. Fr. Inform. Rech. Oper. 4 (1970), pp. 154–159.
  • J.J. Moreau, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. Fr. 93 (1965), pp. 273–299.
  • R.T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res. 1 (1976), pp. 97–116.
  • M. Tao and X.M. Yuan, Recovering low-rank and sparse components of matrices from incomplete and noisy observations, SIAM J. Optim. 21 (2011), pp. 57–81.
  • B.X. Zhang, Z.B. Zhu, and S. Wang, A simple primal-dual method for total variation image restoration, J Vis Commun Image Represent 38 (2016), pp. 814–823.

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