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On the solution of bounded and unbounded mixed complementarity problems

Summary: On the solution of bounded and unbounded mixed
complementarity problems
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


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


Collections: Mathematics