Given real vectors v and r of the same size, what are the following, and how are they duals?

1. inf{v'*inv(R)*v : R>0, diag(R)= r}
2. sup{v'Rv : R>0, diag(R)= r} Note: R > 0 denotes positive definiteness, x' denotes transpose, and inf, and sup are the infimum and supremum.