This article investigates four minimizing the tracking error between the returns of portfolio and a benchmark .All model have in common that absolute deviations are minimized instead of squared deviations as is the case for traditional optimization model .Linear programs are formulated to derive explicit solutions. The model are applied to a portfolio containing six market component indexes and the tracking error with respect to the SSE A share index is minimized.The results are compared to those of aquadratic track ing error optimization technique. The portfolio weights of the optimized portfo lio and its return/risk properties are different across the models which implies that optimization models should be targeted to specific investment objective and be used to measure the rewards to manager of Fund.