  Given a monomial ideal in a polynomial ring over a field, we define the
generalized Newton complementary dual of the given ideal. We show good
properties of such duals including linear quotients and isomorphisms between
the special fiber rings. We construct the cellular free resolutions of duals of
strongly stable ideals generated in the same degree. When the base ideal is
generated in degree two, we provide an explicit description of cellular free
resolution of the dual of a compatible generalized stable ideal.
