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<TITLE>Machine Learning via Polyhedral Concave Minimization </TITLE>
<H2>Machine Learning via Polyhedral Concave Minimization </H2>
 O. L. Mangasarian<BR>
MP-TR-95-20<BR>
November 1995
<p>
 Two fundamental problems of machine learning, misclassification minimization and feature selection, are formulated as the minimization of a concave function on a polyhedral set. Other formulations of these problems utilize linear programs with equilibrium constraints which are generally intractable. In contrast, for the proposed concave minimization formulation, a successive linearization algorithm without stepsize terminates after a maximum average of 7 linear programs on problems with as many as 2124 points in 2082-dimensional space. The algorithm terminates at a stationary point or a global solution to the problem. Preliminary numerical results indicate that the proposed approach is quite effective and more efficient than other approaches.<P>
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