AN INTERIOR-POINT METHOD FOR MULTIFRACTIONAL PROGRAMS WITH CONVEX CONSTRAINTS

We present an interior-point method for a family of multifractional pr ograms with convex constraints. The programs under consideration consi st of minimizing the maximum of a finite number of linear fractions ov er some convex set. First, we present a simple short-step algorithm fo r solving such multifractional programs, and we show that, under suita ble assumptions, the convergence of the short-step algorithm is weakly polynomial in a sense specified below. Then, we describe a practical implementation of the proposed method, and we report results of numeri cal experiments with this algorithm. These results suggest that the pr oposed method is a viable alternative to the standard Dinkelbach-type algorithms for solving multifractional programs.