 
Summary: On the reformulation of nonlinear complementarity
problems using the FischerBurmeister function
Roberto Andreani \Lambda Jos'e Mario Mart'inez y
October 26, 1998
Abstract
A boundedlevelset result for a reformulation of the boxconstrained
variational inequality problem proposed recently by Facchinei, Fischer
and Kanzow is proved. An application of this result to the (unbounded)
nonlinear complementarity problem is suggested.
Keywords. Complementarity, unconstrained minimization, reformu
lation.
AMS: 90C33, 90C30
1 Main results
Given F : IR n ! IR n , F 2 C 1 (IR n ), the boxconstrained variational inequality
problem (BVIP) consists on finding x
2\Omega such that
hF (x); z \Gamma xi – 0 for all z
2\Omega ; (1)
where\Omega is the compact box
\Omega = fx 2 IR n j ` Ÿ x Ÿ rg: (2)
