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}
}
  • O. Güler
  • Published 1 November 1996
  • Mathematics, Computer Science
  • Math. Oper. Res.
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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Characterization of the barrier parameter of homogeneous convex cones
TLDR
The smallest (best) barrier parameter of self-concordant barriers for homogeneous convex cones is characterized and it is proved that this parameter is the same as the rank of the cone which is the number of steps in a recursive construction of the cones.
Hyperbolic Polynomials and Interior Point Methods for Convex Programming
  • O. Güler
  • Mathematics, Computer Science
    Math. Oper. Res.
  • 1997
TLDR
It is shown that the long-step primal potential reduction methods of Nesterov and Todd and the surface-following methods of Wojciech Nemirovskii extend to hyperbolic barrier functions and that there exists a hyperBolic barrier function on every homogeneous cone.
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