  We construct absolute and relative versions of Hamiltonian Floer homology
algebras for strongly semi-positive compact symplectic manifolds with convex
boundary, where the ring structures are given by the appropriate versions of
the pair-of-pants products. We establish the absolute and relative
Piunikhin-Salamon-Schwarz isomorphisms between these Floer homology algebras
and the corresponding absolute and relative quantum homology algebras. As a
result, the absolute and relative analogues of the spectral invariants on the
group of compactly supported Hamiltonian diffeomorphisms are defined.
