Abstract
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 equation-based methods (using the Fischer–Burmeister function) in such a way that we overcome a major drawback of this equation-based method. The resulting nonsmooth Levenberg–Marquardt-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.
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Acknowledgment
The authors would like to thank the referees for some very helpful comments.
Notes
E-mail: [email protected]