First-order methods for constrained convex programming based on linearized augmented Lagrangian function

Yangyang Xu

Optimization and Control mathscidoc:1912.43148

arXiv preprint arXiv:1711.08020, 2017.11
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for constrained convex programs, for which the constraint set is represented by affine equations and smooth nonlinear inequalities. Both methods are based on the classic augmented Lagrangian function. They update the multipliers in the same way as the augmented Lagrangian method (ALM) but employ different primal variable updates. The first method, at each iteration, performs a single proximal gradient step to the primal variable, and the second method is a block update version of the first one.
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@inproceedings{yangyang2017first-order,
  title={First-order methods for constrained convex programming based on linearized augmented Lagrangian function},
  author={Yangyang Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112550913231708},
  booktitle={arXiv preprint arXiv:1711.08020},
  year={2017},
}
Yangyang Xu. First-order methods for constrained convex programming based on linearized augmented Lagrangian function. 2017. In arXiv preprint arXiv:1711.08020. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112550913231708.
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