A first-order block-decomposition method for solving two-easy-block structured semidefinite programs. The paper deals with a new first-order block-decomposition method which is proposed to minimize the sum of convex differentiable functions and convex non-smooth functions. More especially, the authors study the performance of a Block-Decomposition (BD) method based on the BD-hybrid proximal extra-gradient. The main contribution of the paper is two-fold: firstly, the authors introduce an adaptive choice of stepsize for performing an extra-gradient step and then they use a scaling factor to balance the blocks. The method is used to solve four broad classes of conic semi-definite programming, and numerical results illustrate its efficiency.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Alves, M. Marques; Marcavillaca, Raul T.: On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng’s modified forward-backward methods with inertial effects (2020)
  2. Sicre, Mauricio Romero: On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems (2020)
  3. Sun, Defeng; Toh, Kim-Chuan; Yuan, Yancheng; Zhao, Xin-Yuan: SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0) (2020)
  4. Alves, M. Marques; Geremia, Marina: Iteration complexity of an inexact Douglas-Rachford method and of a Douglas-Rachford-Tseng’s F-B four-operator splitting method for solving monotone inclusions (2019)
  5. Chang, Xiaokai; Liu, Sanyang; Zhao, Pengjun: A note on the sufficient initial condition ensuring the convergence of directly extended 3-block ADMM for special semidefinite programming (2018)
  6. Xiao, Yunhai; Chen, Liang; Li, Donghui: A generalized alternating direction method of multipliers with semi-proximal terms for convex composite conic programming (2018)
  7. Marques Alves, Maicon; Svaiter, B. F.: A variant of the hybrid proximal extragradient method for solving strongly monotone inclusions and its complexity analysis (2016)
  8. O’Donoghue, Brendan; Chu, Eric; Parikh, Neal; Boyd, Stephen: Conic optimization via operator splitting and homogeneous self-dual embedding (2016)
  9. He, Yunlong; Monteiro, Renato D. C.: Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems (2015)
  10. Sun, Defeng; Toh, Kim-Chuan; Yang, Liuqin: A convergent 3-block semiproximal alternating direction method of multipliers for conic programming with 4-type constraints (2015)
  11. Yang, Liuqin; Sun, Defeng; Toh, Kim-Chuan: SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints (2015)
  12. Jiao, Hong-Wei; Huang, Ya-Kui; Chen, Jing: A novel approach for solving semidefinite programs (2014)
  13. Monteiro, Renato D. C.; Ortiz, Camilo; Svaiter, Benar F.: A first-order block-decomposition method for solving two-easy-block structured semidefinite programs (2014)
  14. Monteiro, Renato D. C.; Ortiz, Camilo; Svaiter, Benar F.: Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems (2014)