Finding the hyperplane that best separates two clusters of points is an important problem in many areas, and particularly in training Support Vector Machines (SVMs). The desirable solution is shown to satisfy an NLP problem with a single nonlinear constraint. Existing methodology transforms this problem to a dual convex QP problem, but is shown to be unreliable in many situations.
A new proposal based on the SQP method is described, along with numerical experience. Potential applications can have a very large number of points in the clusters and are computationally challanging. We outline an approximation scheme based on low-rank Cholesky factors.
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