An extended formulation approach to the edge-weighted maximal clique problem

We consider an extended formulation approach to the edge-weighted maximal clique problem. The problem is formulated by using additional variables for the set of nodes with the natural variables for the set of edges. We show that the proposed formulation is superior to the natural formulation both theoretically and practically. By using the projection technique, we can also derive new classes of facet-defining inequalities for the lower-dimensional polytope of the natural variables. Computational results are reported.