Faster than the fast Legendre transform, the linear-time Legendre transform. An algorithm is proposed for numerical computation of the Legendre-Fenchel transform u∗(s)=supx[⟨s,x⟩−u(x)] with a linear-time complexity in arbitrary space dimensions. A corresponding MATLAB package is described and illustrated with examples. (netlib numeralgo na13)

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Hütter, Jan-Christian; Rigollet, Philippe: Minimax estimation of smooth optimal transport maps (2021)
  2. Jacobs, Matt; Lee, Wonjun; Léger, Flavien: The back-and-forth method for Wasserstein gradient flows (2021)
  3. Jaramillo, Gabriela; Venkataramani, Shankar C.: A modified split Bregman algorithm for computing microstructures through Young measures (2021)
  4. Singh, Shambhavi; Lucet, Yves: Linear-time convexity test for low-order piecewise polynomials (2021)
  5. Carpio, Ronaldo; Kamihigashi, Takashi: Fast value iteration: an application of Legendre-Fenchel duality to a class of deterministic dynamic programming problems in discrete time (2020)
  6. Jacobs, Matt; Léger, Flavien: A fast approach to optimal transport: the back-and-forth method (2020)
  7. Kumar, Deepak; Lucet, Yves: Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time (2019)
  8. Lauster, Florian; Luke, D. Russell; Tam, Matthew K.: Symbolic computation with monotone operators (2018)
  9. Bouillard, Anne; Faou, Erwan; Zavidovique, Maxime: Fast weak-KAM integrators for separable Hamiltonian systems (2016)
  10. Borwein, Jonathan M.; Luke, D. Russell: Duality and convex programming (2015)
  11. Contento, Lorenzo; Ern, Alexandre; Vermiglio, Rossana: A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation (2015)
  12. Fathollahi, Shahin; Ghiura, Adrian; Postolache, Mihai; Rezapour, Shahram: A comparative study on the convergence rate of some iteration methods involving contractive mappings (2015)
  13. Achdou, Yves; Camilli, Fabio; Corrias, Lucilla: On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations (2014)
  14. Gardiner, Bryan; Jakee, Khan; Lucet, Yves: Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions (2014)
  15. Gardiner, Bryan; Lucet, Yves: Computing the conjugate of convex piecewise linear-quadratic bivariate functions (2013)
  16. Lucet, Yves: Techniques and open questions in computational convex analysis (2013)
  17. Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu: Self-dual smooth approximations of convex functions via the proximal average (2011)
  18. Gardiner, Bryan; Lucet, Yves: Graph-matrix calculus for computational convex analysis (2011)
  19. Helluy, P.; Mathis, H.: Pressure laws and fast Legendre transform (2011)
  20. Johnstone, Jennifer A.; Koch, Valentin R.; Lucet, Yves: Convexity of the proximal average (2011)

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