Stationary point conditions for the FB merit function associated with symmetric cones

For the symmetric cone complementarity problem, we show that each stationary point of the unconstrained minimization reformulation based on the Fischer–Burmeister merit function is a solution to the problem, provided that the gradient operators of the mappings involved in the problem satisfy column monotonicity or have the Cartesian P0P0-property. These results answer the open question proposed in the article that appeared in Journal of Mathematical Analysis and Applications 355 (2009) 195–215.