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Area Under the ROC Curve (AUC) is often used to evaluate ranking performance in binary classification problems. Several researchers have approached AUC optimization by approximating the equivalent Wicoxon-Mann-Whitney (WMW) statistic. We present a linear programming approach similar to 1-norm Support Vector Machines (SVMs) for instance ranking by an approximation to the WMW statistic. Our formulation can be applied to nonlinear problems by using a kernel function. Our ranking algorithm outperforms SVMs in both AUC and classification performance when using RBF kernels, but curiously not with polynomial kernels. We experiment with variations of chunking to handle the quadratic growth of the number of constraints in our formulation.