On the Von Neumann Economic Growth Problem

We study the complexity of the von Neumann economic growth problem: $$\gamma^\ast=\max \{\gamma\mid \exists y \ne 0: y \ge 0, B-\gamma Ay \ge 0\},$$ where A and B are given two nonnegative and rational m × n-matrices, and A has no all-zero column. Let the binary data length of A and B be L. We develop an interior-point algorithm to generate a γI„, such that γ*-2-1 ≤ γI„ ≤ γ*, in Om + nL + minm, nt iterations where each iteration solves a system of m + n linear equations.