Alternating direction augmented Lagrangian methods for semidefinite programming

Zaiwen Wen Donald Goldfarb Wotao Yin

Optimization and Control mathscidoc:1912.43774

Mathematical Programming Computation, 2, 203-230, 2010.12
We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our
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@inproceedings{zaiwen2010alternating,
  title={Alternating direction augmented Lagrangian methods for semidefinite programming},
  author={Zaiwen Wen, Donald Goldfarb, and Wotao Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205719058145338},
  booktitle={Mathematical Programming Computation},
  volume={2},
  pages={203-230},
  year={2010},
}
Zaiwen Wen, Donald Goldfarb, and Wotao Yin. Alternating direction augmented Lagrangian methods for semidefinite programming. 2010. Vol. 2. In Mathematical Programming Computation. pp.203-230. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205719058145338.
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