A linear programming technique is introduced that jointly performs feature selection and classifier training so that a subset of features is optimally selected together with the classifier. Because traditional classification methods in computer vision have used a two-step approach: feature selection followed by classifier training, feature selection has often been ad hoc, using heuristics or requiring a time-consuming forward and backward search process. Moreover, it is difficult to determine which features to use and how many features to use when these two steps are separated. The linear programming technique used in this paper, which we call feature selection via linear programming (FSLP), can determine the number of features and which features to use in the resulting classification function based on recent results in optimization. We analyze why FSLP can avoid the curse of dimensionality problem based on margin analysis. As one demonstration of the performance of this FSLP technique for computer vision tasks, we apply it to the problem of face expression recognition. Recognition accuracy is compared with results using Support Vector Machines, the AdaBoost algorithm, and a Bayes classifier.