On Monotonicity in the Scaled Potential Algorithm for Linear-programming

In this note we show that a simple modification of Ye's "affinely scaled potential reduction" algorithm makes the method monotone in the true objective on primal steps. Based on computational experience with the standard form projective algorithm, the monotonicity modification should substantially improve the performance of the algorithm when it is initialized with a lower bound much less than the optimal objective value. Imposing monotonicity on primal steps also results in stronger lower bound updates, which is not the case with the standard form projective algorithm