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<TITLE>Misclassification Minimization </TITLE>
<H2>Misclassification Minimization </H2>
 Olvi L. Mangasarian<BR>
CS-TR-93-1186<BR>
October 1993
<p>
 The problem of minimizing the number of misclassified points by a plane, attempting to separate two point sets with intersecting convex hulls in $n$-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed for the penalty problem that terminates at a stationary point or a global solution. Novel aspects of the approach include: (i) A linear complementarity formulation of the step function that ``counts'' misclassifications, (ii) Exact penalty formulation without boundedness, nondegeneracy or constraint qualification assumptions, (iii) An exact solution extraction from the sequence of minimizers of the penalty function for a finite value of the penalty parameter for the general LPEC and an explicitly exact solution for the LPEC with uncoupled constraints, and (iv) A parametric quadratic programming formulation of the LPEC associated with the misclassification minimization problem.<P>
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