Sinkhorn algorithms and linear programming solvers for optimal partial transport problems
This work addresses incremental improvements in computational methods for transport problems, primarily relevant to researchers in optimization and machine learning.
The authors tackled the generalization of optimal partial transport problems by introducing function-based mass terms, and they developed dual formulations, Sinkhorn solvers, and linear programming solvers for these scenarios.
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.