# Barrier Functions in Interior Point Methods

@article{Gler1996BarrierFI, title={Barrier Functions in Interior Point Methods}, author={Osman G{\"u}ler}, journal={Math. Oper. Res.}, year={1996}, volume={21}, pages={860-885} }

We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some known barriers as the universal barrier scaled by an appropriate constant. We also calculate some new…

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## 174 Citations

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