An interior-point method for fractional programs with convex constraints

The authors present an interior-point method for a class of fractional programs with convex constraints. The poposed 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 sets 𝒞k containing the origin and certain projections of the optimal points, and the area of 𝒞k is reduced by a constant factor c<1 at each iteration. The factor c depends only on the self-concordance parameter of a barrier function associated with the feasible set. The authors present an outline of a practical implementation of the proposed method, and they report results of some preliminary numerical experiments.