Appl Math Optim 43:1–19 (2001)
2001 Springer-Verlag New York Inc.
Solution of a General Linear Complementarity Problem
Using Smooth Optimization and Its Application to
Bilinear Programming and LCP
and J. J´udice
Escola Superior de Tecnologia de Tomar,
2300 Tomar, Portugal
Departamento de Matem´atica Aplicada, Universidade de Campinas,
Departamento de Matem´atica Aplicada, Faculdade de Ciencias,
Universidade do Porto, 4000 Porto, Portugal
Departamento de Matem´atica, Universidade de Coimbra,
3000 Coimbra, Portugal
Abstract. This paper addresses a General Linear Complementarity Problem
(GLCP) that has found applications in global optimization. It is shown that a solu-
tion of the GLCP can be computed by ﬁnding a stationary point of a differentiable
function over a set deﬁned by simple bounds on the variables. The application of
this result to the solution of bilinear programs and LCPs is discussed. Some com-
putational evidence of its usefulness is included in the last part of the paper.
Key Words. Global optimization, Linear complementarity problems, Bilinear
programming, Box constrained optimization.
AMS Classiﬁcation. 90C33 (65K05, 49M15).
The General Linear Complementarity Problem (GLCP) consists of ﬁnding vectors z ∈
and y ∈ R
q + Mz+ Ny≥ 0, (1)
Support of this work has been provided by project PRAXIS XXI 2/2.1/MAT/346/94, Portugal. The
second author was supported by CNPq and Fapesp.