A Newton algorithm for semi-discrete optimal transport

@article{Kitagawa2019ANA,
  title={A Newton algorithm for semi-discrete optimal transport},
  author={Jun Kitagawa and Quentin M{\'e}rigot and Boris Thibert},
  journal={ArXiv},
  year={2019},
  volume={abs/1603.05579}
}
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We refer to this setting as semi-discrete optimal transport. Among the several algorithms proposed to solve semi-discrete optimal… 

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