Merit functions for semi-definite complementarity problems

Merit functions such as the gap function, the regularized gap function, the implicit Lagrangian, and the norm squared of the Fischer–Burmeister function have played an important role in the solution of complementarity problems defined over the cone of nonnegative real vectors. We study the extension of these merit functions to complementarity problems defined over the cone of block-diagonal symmetric positive semi-definite real matrices. The extension suggests new solution methods for the latter problems.