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A homotopy method for mixed complementarity problems based on the PATH solver. (English) Zbl 0952.65050
Griffiths, D. F. (ed.) et al., Numerical analysis 1999. Proceedings of the 18th Dundee biennial conference, Univ. of Dundee, GB, June 29th - July 2nd, 1999. Boca Raton, FL: Chapman & Hall/ CRC. Chapman Hall/CRC Res. Notes Math. 420, 143-167 (2000).
Summary: 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 \(\mathbb{R}^n\), 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.
For the entire collection see [Zbl 0938.00012].

65K05 Numerical mathematical programming methods
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations