@InCollection{FraSonWer11, author={Vojtech Franc and Soeren Sonnenburg and Tomas Werner}, title={Cutting Plane Methods in Machine Learning}, booktitle={Optimization for Machine Learning}, publisher={MIT Press}, address = {Cambridge, MA.}, year={2011}, editor={Suvrit Sra and Sebastian Nowozin and Stephen J. Wright}, pdf={ftp://cmp.felk.cvut.cz/pub/cmp/articles/franc/Franc-MITchapter-2011.pdf}, abstract={Cutting plane methods are optimization techniques that incrementally construct an approximation of a feasible set or an objective function by linear inequalities, called cutting planes. Numerous variants of this basic idea are among standard tools used in convex nonsmooth optimization and integer linear programing. Recently, cutting plane methods have seen growing interest in the field of machine learning. In this chapter, we describe the basic theory behind these methods and we show three of their successful applications to solving machine learning problems: regularized risk minimization, multiple kernel learning, and MAP inference in graphical models.}