A fast computational algorithm for the Legendre-Fenchel transform

@article{Lucet1996AFC,
  title={A fast computational algorithm for the Legendre-Fenchel transform},
  author={Yves Lucet},
  journal={Comp. Opt. and Appl.},
  year={1996},
  volume={6},
  pages={27-57}
}
We investigate a fast algorithm, introduced by Brenier. which computes the Legendre-Fenchel transform of a real-valued function. We generalize his work to boxed domains and introduce a parameter in order to build an iterative algorithm. The new approach of separating primal and dual spaces allows a clearer understanding of the algorithm and yields better numerical behavior. We extend known complexity results and give new ones about the convergence of the algorithm. 
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