An Interior-Point Method for Multi-fractional Programs with Convex Constraints.

We present an interior-point method for a family of multi-fractional programs with convex constraints. The programs under consideration consist of minimizing the maximum of a finite number of linear fractions over some convex set. First, we present a simple "short-step" algorithm for solving such multi-fractional programs. Then, we describe a practical implementation of the proposed method, and we report results of numerical experiments with this algorithm. These results show that the proposed method is a viable alternative to the standard Dinkelbach-type algorithms for solving multi-fractional programs. We also present some theoretical results for the short-step variant of our interior-point methods. In particular, it is shown that, under additional assumptions, the short-step algorithm converges in polynomial time. Here the convergence rate depends very weakly on the data of the problem.