We introduce a new algorithm for the solution of the mixed complementarity
problem (MCP) which has stronger properties than most existing methods. In
fact, typical solution methods for the MCP either generate feasible iterate
s but have to solve relatively complicated subproblems (like quadratic prog
rams or linear complementarity problems), or they have relatively simple su
bproblems (like linear systems of equations) but generate not necessarily f
easible iterates. The method to be presented here combines the nice feature
s of these two classes of methods: It has to solve only one linear system o
f equations (of reduced dimension) at each iteration, and it generates feas
ible (more precisely: strictly feasible) iterates. The new method has some
nice global and local convergence properties. Some preliminary numerical re
sults will also be given.