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Machine learning via polyhedral concave minimization. (English) Zbl 0906.68127
Fischer, Herbert (ed.) et al., Applied mathematics and parallel computing. Festschrift for Klaus Ritter. Heidelberg: Physica. 175-188 (1996).
Summary: 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 4192 points in 14-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.
For the entire collection see [Zbl 0895.00068].

MSC:
68T05 Learning and adaptive systems in artificial intelligence
Software:
GAMS; MINOS
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