AN INTERIOR-POINT METHOD FOR FRACTIONAL PROGRAMS WITH CONVEX CONSTRAINTS

We present an interior-point method for a class of fractional programs with convex constraints. The proposed algorithm converges at a polyno mial rate, similarly as in the case of a convex problem, even though f ractional programs are only pseudo-convex. Here, the rate of convergen ce is measured in terms of the area of two-dimensional convex sets C-k containing the origin and certain projections of the optimal points, and the area of C-k is reduced by a constant factor c<1 at each iterat ion, The factor c depends only on the self-concordance parameter of a barrier function associated with the feasible set. We present an outli ne of a practical implementation of the proposed method, and we report results of some preliminary numerical experiments.