On the von Neumann economic growth problem

We study the complexity of the von Neumann economic growth problem: γ*:=max{γ|∃y≠0: y≥0, (B–γA)y≥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 γ, such that γ*–2^–1≤γ≤γ* in O((m+n)(L+min(m, n)t)) iterations where each iteration solves a system of (m+n) linear equations.