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

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.

E-mail: [email protected]

Keywords:

• Complementarity problems
• Nonlinear least squares reformulation
• Semismooth functions
• Global convergence
• Quadratic convergence

Acknowledgment

The authors would like to thank the referees for some very helpful comments.

Notes

E-mail: [email protected]