A cutting plane algorithm for semi-definite programming problems with applications to failure discriminant analysis

We will propose a new cutting plane algorithm for solving a class of semi-definite programming problems (SDP) with a small number of variables and a large number of constraints. Problems of this type appear when we try to classify a large number of multi-dimensional data into two groups by a hyper-ellipsoidal surface. Among such examples are cancer diagnosis, failure discrimination of enterprises. Also, a certain class of option pricing problems can be formulated as this type of problem. We will show that the cutting plane algorithm is much more efficient than the standard interior point algorithms for solving SDP.