Asymptotic Behavior of Continuous Trajectories for Primal-Dual Potential-Reduction Methods

This article considers continuous trajectories of the vector fields induced by primaldual potential-reduction algorithms for solving linear programming problems. It is known that these trajectories converge to the analytic center of the primal-dual optimal face. We establish that this convergence may be tangential to the central path, tangential to the optimal face, or in between, depending on the value of the potential function parameter.