Year: 2026
Type: article
Abstract: . Motivated by the success of Sinkhorn’s algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish exponential convergence guarantees for the IPFP whenever the set of probability measures which is projected onto is defined through constraints arising from linear function spaces. This unifies and extends recent results from multimarginal, adapted, and martingale optimal transport. The proofs are based on strong convexity arguments for the dual problem, and the key contribution is to illuminate the role of the geometric interplay between the subspaces defining the constraints. In this regard, we show that the larger the angle (in the sense of Friedrichs) between the linear function spaces, the better the rate of contraction of the IPFP.
Source: SIAM Journal on Optimization
DOI: 10.1137/25m1752584
Authors: Stephan Eckstein, Aziz Lakhal
Institution: University of Tübingen
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G8115564757
OpenAlex ID: W4416150574
FWCI:
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