## Machine Learning via Polyhedral Concave Minimization (1996)

Citations: | 27 - 12 self |

### BibTeX

@MISC{Mangasarian96machinelearning,

author = {O. L. Mangasarian},

title = {Machine Learning via Polyhedral Concave Minimization},

year = {1996}

}

### Years of Citing Articles

### OpenURL

### Abstract

Two fundamental problems of machine learning, misclassification minimization [10, 24, 18] and feature selection, [25, 29, 14] are formulated as the minimization of a concave function on a polyhedral set. Other formulations of these problems utilize linear programs with equilibrium constraints [18, 1, 4, 3] 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 4192 points in 14dimensional 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. 1 Introduction We shall consider the following two fundamental problems of machine learning: Problem 1.1 Misclassification Minimization [24, 18] Given two finite point sets A and B in the n-dimensional real s...