Summary: Mathematical Programming manuscript No.
(will be inserted by the editor)
R. Andreani · J. J. J´udice · J. M.
Mart´inez · J. Patr´icio
On the natural merit function for
solving complementarity problems
Received: 01/10/2007 / Accepted: date
Abstract Complementarity problems may be formulated as nonlinear sys-
tems of equations with non-negativity constraints. The natural merit function
is the sum of squares of the components of the system. Sufficient conditions
are established which guarantee that stationary points are solutions of the
complementarity problem. Algorithmic consequences are discussed.
Keywords Complementarity Problems · Merit functions · Nonlinear
Mathematics Subject Classification (2000) 78M50 · 90C30
Research of J. J. J´udice and J. Patr´icio was partially supported by Project
POCI/MAT/56704/2004 of the Portuguese Science and Technology Foundation. J.
M. Mart´inez and R. Andreani were supported by FAPESP and CNPq (Brazil).