  We prove two relative local variational principles of topological pressure
functions $P(T,\mathcal{F},\mathcal{U},y)$ and$P(T,\mathcal{F},\mathcal{U}|Y)$
for a given factor map $\pi$, an open cover $\mathcal{U} $ and a subadditive
sequence of real-valued continuous functions $\mathcal{F}$. By proving the
upper semi-continuity and affinity of the entropy maps
$h_{\{\cdot\}}(T,\mathcal{U}\mid Y)$ and $h^+_{\{\cdot\}}(T,\mathcal{U}\mid Y)$
on the space of all invariant Borel probability measures, we show that the
relative local pressure $P(T,\mathcal{\{\cdot\}},\mathcal{U}|Y)$ for
subadditive potentials determines the local measure-theoretic conditional
entropies.
