potential functions

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

  • Reha H. Tütüncü
    • Categories Linear Programming Tags , , , ,

    This article considers continuous trajectories of the vector fields induced by primal-dual 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, … Read more

    Continuous trajectories for primal-dual potential-reduction methods

  • Reha H. Tütüncü
    • Categories Linear Programming Tags , ,

    This article considers continuous trajectories of the vector fields induced by two different primal-dual potential-reduction algorithms for solving linear programming problems. For both algorithms, it is shown that the associated continuous trajectories include the central path and the duality gap converges to zero along all these trajectories. For the algorithm of Kojima, Mizuno, and Yoshise, … Read more