Error Bounds for Linear Matrix Inequalities

@article{Sturm2000ErrorBF,
  title={Error Bounds for Linear Matrix Inequalities},
  author={Jos F. Sturm},
  journal={SIAM Journal on Optimization},
  year={2000},
  volume={10},
  pages={1228-1248}
}
For iterative sequences that converge to the solution set of a linear matrix inequality, we show that the distance of the iterates to the solution set is at most O(2 ?d). The nonnegative integer d is the so{called degree of singularity of the linear matrix inequality, and denotes the amount of constraint violation in the iterate. For infeasible linear matrix inequalities, we show that the minimal norm of {approximate primal solutions is at least 1=O(1=(2 d ?1)), and the minimal norm of… CONTINUE READING

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