Finding the dual problem of minimization problems involving polyconvex integrands (instead of convex integrands), remains an outstanding problem in the calculus of variations. Duality is a powerful tool for studying uniqueness and stability of minimizers, and for writing the Euler-Lagrange equations when standard growth conditions, as imposed by C.B. Morrey in his pioneer work in 1952, fail to hold. In this talk, motivated by integrands which appear in the study of Ogden material, we consider a collection of discrete variational problems which would help tackling some of the challenges in the calculus of variations.