An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Optimization

@article{Kheirfam2015AnAI,
  title={An Adaptive Infeasible Interior-Point Algorithm with Full Nesterov-Todd Step for Semidefinite Optimization},
  author={Behrouz Kheirfam},
  journal={Journal of Mathematical Modelling and Algorithms in Operations Research},
  year={2015},
  volume={14},
  pages={55-66}
}
  • B. Kheirfam
  • Published 1 March 2015
  • Computer Science
  • Journal of Mathematical Modelling and Algorithms in Operations Research
We present an adaptive full Nesterov-Todd step infeasible interior-point method for semidefinite optimization. The proposed algorithm requires two types of full Nesterov-Todd steps are called, feasibility steps and centering steps, respectively. At each iteration both feasibility and optimality are reduced exactly at the same rate. In each iteration of the algorithm we use the largest possible barrier parameter value θ. The value θ varies from iteration to iteration and it lies between the two… 
3 Citations

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This paper shows that, in addition to the predictor step, each corrector step decreases the duality gap as well, and proves that the iteration complexity of the proposed algorithm coincides with the best iteration bound for small neighbourhood algorithms that use the Nesterov–Todd direction.

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