In this talk, we discuss the von Neumann algorithm for linear programming. In particular, we analyze the convergence of the algorithm and provide some insights about the reasons for its slow convergence. We then present new algorithmic ideas that aim at accelerating the convergence of the von Neumann algorithm. We also show how to reduce any linear programming problem to the "standard" form of the von Neumann algorithm. Finally, we present numerical results on linear programming problems from the netlib library that show the improvements obtained by the algorithms proposed over the von Neumann algorithm.
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