Limiting behavior of weighted central paths in linear programming

The paper studies the limiting behavior of the weighted central paths in linear programming at both and . It establishes the existence of a partition of the index set such that and as for and , and converge to weighted analytic centers of certain polytopes. For all , the paper shows that the order derivatives and converge when and . Consequently, the derivatives of each order are bounded in the interval . The paper calculates the limiting derivatives explicitly, and establish the surprising result that all higher order derivatives converge to zero when.