Summary: Box-constrained minimization reformulations of complementarity
problems in second-order cones
S. A. Santos¶
January 24, 2006
Reformulations of a generalization of a second-order cone complementarity problem (GSOCCP) as
optimization problems are introduced, that preserve differentiability. Equivalence results are proved in the
sense that the global minimizers of the reformulations with zero objective value are solutions to the GSOCCP
and vice versa. Since the optimization problems involved include only simple constraints, a whole range of
minimization algorithms may be used to solve the equivalent problems. Taking into account that optimization
algorithms usually seek stationary points, a theoretical result is established that ensures equivalence between
stationary points of the reformulation and solutions to the GSOCCP. Numerical experiments are presented
that illustrate the advantages and disadvantages of the reformulations.
Keywords. complementarity problems, minimization algorithms, reformulations.
AMS: 90C33, 90C30
Given F, G : Rn
, we consider the following generalized second-order cone complemen-