Dual Block Gradient Ascent for Entropically Regularised Quantum Optimal Transport

2025/03/22 by Randig, Marvin, von Renesse, Max
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.17590

Abstract

We present a block gradient ascent method for solving the quantum optimal transport problem with entropic regularisation similar to the algorithm proposed in [D. Feliciangeli, A. Gerolin, L. Portinale: J. Funct. Anal. 285 (2023), no. 4, 109963] and [E. Caputo, A. Gerolin, N. Monina, L. Portinale: arXiv:2409.03698]. We prove a linear convergence rate based on strong concavity of the dual functional and present some results of numerical experiments of an implementation.

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