Orlicz Space Regularization of Continuous Optimal Transport Problems

Abstract In this work we analyze regularized optimal transport problems in the so-called Kantorovich form, i.e. given two Radon measures on compact sets, aim is to find a plan, which another measure product of that has these as marginals and minimizes sum certain linear cost function regularization term. We focus terms where Young’s applied (density the) plan integrated against measure. This forces belong Orlicz space. The predual problem derived proofs for strong duality existence primal solutions are presented. Existence (pre-)dual shown special case $$L^p$$ L p -regularization $$p\ge 2$$ ≥ 2 . Moreover, results regarding $$\varGamma $$ Γ -convergence stated: first concerned with do not lie appropriate space guarantees original problem, when smoothing marginals. second result gives convergence discretized unregularized, continuous problem.