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Abstract : |
We present an interior-point method for convex fractional programming. The proposed algorithm converges in polynomial time, just as in the case of a convex problem, even though convex fractional programs are only pseudo-convex. More precisely, the rate of convergence is measured in terms of the area of two-dimensional convex sets C k containing the optimal points, and the area of C k 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. We present an outline of a practical implementation of the proposed method, and we report results of a few numerical experiments. 1., |
