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On interior-point methods for fractional
programs and their convex reformulation

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R.W. Freund, F. Jarre and S. Schaible

We consider the problem of minimizing a convex-concave fraction
subject to convex constraints, using interior-point methods.
The problem can be solved by applying an interior-point method
directly to the original nonconvex problem, or by applying an
interior-point method to an equivalent convex reformulation of
the original problem.
In this paper, these two approaches are compared, and it is shown
that the rate of convergence is of the same order in both cases.
As our main result, we determine the optimal coefficients
in the construction of a self-concordant barrier function for
the convex reformulation of the original problem.
AT&T Numerical Analysis Manuscript No. 94-17,
Bell Laboratories, Murray Hill, New Jersey, November 1994.