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)

Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas

Collections: Mathematics