  In this note, we generalize the classical optimal partial transport (OPT)
problem by modifying the mass destruction/creation term to function-based
terms, introducing what we term ``generalized optimal partial transport''
problems. We then discuss the dual formulation of these problems and the
associated Sinkhorn solver. Finally, we explore how these new OPT problems
relate to classical optimal transport (OT) problems and introduce a linear
programming solver tailored for these generalized scenarios.
