Multi-marginal Entropy-Transport with repulsive cost

2019/07/18 by Gerolin, Augusto, Kausamo, Anna, Rajala, Tapio
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1907.07900

Abstract

In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the Γ-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.

Related

• Duality theory for multi-marginal optimal transport with repulsive costs\n in metric spaces
• Weak Optimal Entropy Transport Problems
• Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures
• Kantorovich duality for general transport costs and applications
• Relaxed multi-marginal costs and quantization effects