A Penalized Fischer - Burmeister Ncp - Function : Theoretical Investigation and Numerical Results 1
نویسندگان
چکیده
We introduce a new NCP-function that reformulates a nonlinear com-plementarity problem as a system of semismooth equations (x) = 0. The new NCP-function possesses all the nice properties of the Fischer-Burmeister function for local convergence. In addition, its natural merit function (x) = 1 2 (x) T (x) has all the nice features of the Kanzow-Yamashita-Fukushima merit function for global convergence. In particular, the merit function has bounded level sets for a monotone complementarity problem with a strictly feasible point. This property allows the existing semismooth Newton methods to solve this important class of comple-mentarity problems without additional assumptions. We investigate the properties of a semismooth Newton-type method based on the new NCP-function and apply the method to a large class of complementarity problems. The numerical results indicate that the new algorithm is extremely promising.
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