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 21 articles , 1 standard article )

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  1. Borwein, Jonathan M.; Luke, D.Russell: Duality and convex programming (2015)
  2. 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)
  3. Fathollahi, Shahin; Ghiura, Adrian; Postolache, Mihai; Rezapour, Shahram: A comparative study on the convergence rate of some iteration methods involving contractive mappings (2015)
  4. Achdou, Yves; Camilli, Fabio; Corrias, Lucilla: On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations (2014)
  5. Gardiner, Bryan; Jakee, Khan; Lucet, Yves: Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions (2014)
  6. Gardiner, Bryan; Lucet, Yves: Computing the conjugate of convex piecewise linear-quadratic bivariate functions (2013)
  7. Lucet, Yves: Techniques and open questions in computational convex analysis (2013)
  8. Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu: Self-dual smooth approximations of convex functions via the proximal average (2011)
  9. Gardiner, Bryan; Lucet, Yves: Graph-matrix calculus for computational convex analysis (2011)
  10. Helluy, P.; Mathis, H.: Pressure laws and fast Legendre transform (2011)
  11. Johnstone, Jennifer A.; Koch, Valentin R.; Lucet, Yves: Convexity of the proximal average (2011)
  12. Oberman, Adam; Osher, Stanley; Takei, Ryo; Tsai, Richard: Numerical methods for anisotropic mean curvature flow based on a discrete time variational formulation (2011)
  13. Gardiner, Bryan; Lucet, Yves: Convex hull algorithms for piecewise linear-quadratic functions in computational convex analysis (2010)
  14. Zhao, Yun-Bin: Convexity conditions and the Legendre-fenchel transform for the product of finitely many positive definite quadratic forms (2010)
  15. Borwein, Jonathan M.; Hamilton, Chris H.: Symbolic Fenchel conjugation (2009)
  16. Lucet, Yves; Bauschke, Heinz H.; Trienis, Mike: The piecewise linear-quadratic model for computational convex analysis (2009)
  17. Oberman, Adam M.: Computing the convex envelope using a nonlinear partial differential equation (2008)
  18. Helluy, Philippe; Seguin, Nicolas: Relaxation models of phase transition flows (2006)
  19. Lucet, Yves: Fast Moreau envelope computation I: Numerical algorithms (2006)
  20. Hiriart-Urruty, J.-B.; Martínez-Legaz, J.-E.: New formulas for the Legendre-Fenchel transform. (2003)

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