On the Connection between Dynamical Optimal Transport and Functional Lifting

• URL: http://arxiv.org/abs/2007.02587v1
• Date: Mon, 6 Jul 2020 08:53:35 GMT
• Title: On the Connection between Dynamical Optimal Transport and Functional Lifting
• Authors: Thomas Vogt, Roland Haase, Danielle Bednarski, Jan Lellmann
• Abstract summary: In this work, we investigate a mathematically rigorous formulation based on embedding into the space over a fixed range $Gamma$ By modifying the continuity equation, the approach can be extended to models with higher-order regularization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the space of pointwise probability measures over a fixed range $\Gamma$. Interestingly, this approach can be derived as a generalization of the theory of dynamical optimal transport. Imposing the established continuity equation as a constraint corresponds to variational models with first-order regularization. By modifying the continuity equation, the approach can also be extended to models with higher-order regularization.

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