Karmarkar's algorithm with improved steps

We define a function of the interior of the feasible region of Karmarkar's canonical linear program with the property that its supremum is bounded above by one, if and only if the optimal value of the linear program is zero. We use this function to obtain data-dependent steps for Karmarkar's algorithm. The corresponding reduction in the potential function improves upon the data-independent reduction derived by Padberg. We analyze the general step and consider its potential practical advantages.