A Newton-CG Augmented Lagrangian Method for Semidefinite Programming

@article{Zhao2010ANA,
  title={A Newton-CG Augmented Lagrangian Method for Semidefinite Programming},
  author={Xin-Yuan Zhao and Defeng Sun and Kim-Chuan Toh},
  journal={SIAM Journal on Optimization},
  year={2010},
  volume={20},
  pages={1737-1765}
}
We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of the generalized Hessian of the objective function in these inner problems, a key property for ensuring… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 42 REFERENCES

Regularization Methods for Semidefinite Programming

  • SIAM Journal on Optimization
  • 2009
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

An Augmented Primal-Dual Method for Linear Conic Programs

  • SIAM Journal on Optimization
  • 2008
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Solving Lift-and-Project Relaxations of Binary Integer Programs

  • SIAM Journal on Optimization
  • 2006
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

A nonsmooth version of Newton's method

  • Math. Program.
  • 1993
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

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