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A lecture by Shmuel Friedland from the University of Illinois at Chicago exploring barrier relaxations of classical and quantum optimal transport problems. Recorded on May 23, 2025, as part of IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Discover how entropic relaxation has advanced multi-partite optimal transport problems (MPOTP) over the past fifteen years, enabling faster solutions through Sinkhorn-type algorithms. Learn how similar approaches apply to quantum MPOTP, though with more complex rescaling algorithms. Examine how interior point methods (IPM) for primary and dual problems function as barrier relaxations, with particular focus on the advantages of dual OTP approaches that require fewer variables. Compare the efficiency of IPM methods versus Sinkhorn algorithms in both classical and quantum contexts, noting that while IPM isn't as fast for classical problems, it shows promising efficiency for quantum MPOTP applications.
