The discrete-time portfolio optimization problem with proportional transaction costs is considered. By formulating this problem as a Markov decision problem, the difference of the long-run average growth rate of total wealth of two different policies is obtained by using a sensitivity-based approach. By analyzing the structure of the difference formula, the optimality equation and the policy iteration algorithm for the optimal investment policy can be intuitively derived. Thereby the on-line implementation of the policy iteration algorithm is designed. A numerical example illustrates the effectiveness of the proposed algorithm.