A new polynomial-time algorithm for linear programming
Combinatorica
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As described in Goldfarb and Mehrotra [3], the convergence analysis of Karmarkar's method for linear programming leads naturally to an acceptance criterion when approximate projections are used in the course of the algorithm. Unfortunately, the preliminary results of Goldfarb and Mehrotra indicate that their criterion is generally not strong enough to insure that the algorithm makes reasonable progress. In this note we present a stronger criterion and show that the difference between the two criteria is potentially large.