Abstract
We present an interior-point method for a class of fractional programs with convex constraints. The proposed algorithm converges at a polynomial rate, similarly as in the case of a convex problem, even though fractional programs are only pseudo-convex. Here, the rate of convergence is measured in terms of the area of two-dimensional convex setsC k containing the origin and certain projections of the optimal points, and the area ofC k is reduced by a constant factorc < 1 at each iteration. The factorc depends only on the self-concordance parameter of a barrier function associated with the feasible set. We present an outline of a practical implementation of the proposed method, and we report results of some preliminary numerical experiments.
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Freund, R.W., Jarre, F. An interior-point method for fractional programs with convex constraints. Mathematical Programming 67, 407–440 (1994). https://doi.org/10.1007/BF01582229
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DOI: https://doi.org/10.1007/BF01582229