  It is known that optical-lattice (OL) potentials can stabilize solitons and
solitary vortices against the critical collapse, generated by the cubic
attractive nonlinearity in the 2D geometry. We demonstrate OLs can also
stabilize various species of fundamental and vortical solitons against the
super-critical collapse, driven by the double-attractive cubic-quintic
nonlinearity (however, solitons remain unstable in the case of the pure quintic
nonlinearity). Two types of OLs are considered, producing similar results: the
2D Kronig-Penney "checkerboard", and the sinusoidal potential. Soliton families
are obtained by means of a variational approximation, and as numerical
solutions. The stability of the families, which include fundamental and
multi-humped solitons, vortices of oblique and straight types, vortices built
of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov
criterion. The model applies to optical media and BEC in "pancake" traps.
