The perceptron and von Neumann algorithms are known to be closely related, like duals. A deterministic rescaled version of the perceptron algorithm was proved to be polynomial by Pena and Soheil. Recently, Chubanov proposed a method which solves homogeneous linear equality systems with positive variables in polynomial time. Chubanov's method can be considered as a column-wise rescaling procedure. We adapt Chubanov's method to the von Neumann problem, and so we design a polynomial time column-wise rescaling von Neumann algorithm. This algorithm is the first variant of the von Neumann algorithm with polynomial complexity.
Joint work with Dan Li and Kees Roos