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Mathematical programming approaches were applied to a variety of problems in machine learning in order to gain deeper understanding of the problems and to come up with new and more efficient computational algorithms. Theoretical and/or computational contributions were made to Data Envelopment Analysis wherein one seeks efficient decision making units, Neural Networks with as few hidden units as possible, optimization problems subject to constraints that in turn require the solution of further optimization problems, classification algorithms that suppress unnecessary or redundant features, algorithms that chunk massive data sets in order to classify them, clustering data based on the novel concept of nearness to cluster planes rather than cluster centroids, a new implementable general theory for Support Vector Machines that does away with the restrictive Mercer positive definite kernel condition that had hitherto been universally assumed, a very effective Successive Over Relaxation (SOR) algorithm for solving very large linear and nonlinear kernel classification problems, applying support vector machines to breast cancer diagnosis and prognosis, smoothing algorithms for solving large and complex classification problems, nonlinear data fitting using support vector machines and a robust loss function, and classifying data that is partly labeled and partly unlabeled.