Low-order penalty equations for semidefinite linear complementarity problems

We extend the power penalty method for linear complementarity problem (LCP) (Wang and Yang, 2008) to the semidefinite linear complementarity problem (SDLCP). We establish a family of low-order penalty equations for SDLCPs. Under the assumption that the involved linear transformation possesses the Cartesian P-property, we show that when the penalty parameter tends to infinity, the solution to any equation of this family converges to the solution of the SDLCP exponentially. Numerical experiments verify this convergence result.