%A Michael C. Ferris %A Todd S. Munson %A Danny Ralph %T A homotopy method for mixed complementarity problems based on the PATH solver %D October 1999 %R 99-09 %I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN %C MADISON, WI %X Mixed complementarity problems can be recast as zero finding problems for the normal map, a function that is smooth on the interior of each of the cells of a piecewise linear manifold of $\real^n$, called the normal manifold. We develop a predictor-corrector, or path following, homotopy method based upon using piecewise linear approximations to the piecewise smooth normal map. A description of an implementation using technology found in the PATH solver is given along with computational experience on the MCPLIB test suite.