Strictly feasible equation-based methods for mixed complementarity problems

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.