On a semismooth least squares formulation of complementarity problems with gap reduction

We present a nonsmooth least squares reformulation of the complementarity problem and investigate its convergence properties. The global and local fast convergence results (under mild assumptions) are similar to some existing equation-based methods. In fact, our least squares formulation is obtained by modifying one of these equationbased methods (using the Fischer-Burmeister function) in such a way that we overcome a major drawback of this equation-based method. The resulting nonsmooth LevenbergMarquardt-type method turns out to be significantly more robust than the corresponding equation-based method. This is illustrated by our numerical results using the MCPLIB test problem collection.