ON THE VON-NEUMANN ECONOMIC-GROWTH PROBLEM

We study the complexity of the von Neumann economic growth problem: ga mma := max{gamma\reversed capital E y not equal 0: y greater than or equal to 0, (B - gamma A)y greater than or equal to 0} where A and B a re given two nonnegative and rational m X n-matrices, and A has no all -zero column. Let the binary data length of A and B be L. We develop a n interior-point algorithm to generate a <(gamma)over bar>, such that gamma - 2(-1) less than or equal to <(gamma)over bar> less than or eq ual to gamma, in O((m + n)(L + min(m, n)t)) iterations where each ite ration solves a system of (m + n) linear equations.