Optimization plays a significant role in data mining: the process of analyzing data in order to extract useful patterns and relations such as clusters and classes. Clustering, a major branch of unsupervised machine learning, is amenable to a fruitful application of optimization theory. This leads to effective algorithms such as the k-median clustering algorithm and novel methods for the suppression of irrelevant features in clustering. Classification on the other hand, a mainstay of supervised machine learning and data mining, is an extremely rich field of application for optimization theory and its algorithms. Support vector machines ($SVM$s) constitute the core of modern classification theory. $SVM$s have been extensively used in the last decade, even though they were introduced some forty years ago. Through the use of nonlinear kernel functions, SVMs are powerful tools not only in classification theory but also in function approximation as well as nonconvex function optimization. Kernels allow the introduction of complex nonlinear structures into classifiers and nonlinear function approximation by using linear programming only. \vskip .1in \noindent Topics such as the above will be presented as well as applications to medicine and bioinformatics.