On the Von Neumann Economic Growth Problem
Published Online:1 Aug 1995https://doi.org/10.1287/moor.20.3.617
Abstract
We study the complexity of the von Neumann economic growth problem:
$$\gamma^\ast=\max \{\gamma\mid \exists y \ne 0: y \ge 0, (B - \gamma A)y \ge 0\},$$
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 γ̄, such that γ* − 2−1 ≤ γ̄ ≤ γ*, in O((m + n)(L + min(m, n)t)) iterations where each iteration solves a system of (m + n) linear equations.
