Summary: On the solution of bounded and unbounded mixed
Roberto Andreani \Lambda Jos'e Mario Mart'inez y
November 5, 1999
A reformulation of the bounded mixed complementarity problem
is introduced. It is proved that the level sets of the objective function
are bounded and, under reasonable assumptions, stationary points co
incide with solutions of the original variational inequality problem.
Therefore, standard minimization algorithms applied to the new refor
mulation must succeed. This result is applied to the compactification
of unbounded mixed complementarity problems.
Keywords. Mixed complementarity problem, variational inequalities,
box constrained minimization, reformulation.
AMS: 90C33, 90C30
\Lambda Department of Computer Science and Statistics, University of the State of S. Paulo
(UNESP), C.P. 136, CEP 15054000, S~ao Jos'e do Rio PretoSP, Brazil. This author
was supported by FAPESP (Grant 99/083814) and CNPq (Grant 301115/966). Email:
y Department of Applied Mathematics, IMECCUNICAMP, University of Camp