Geodesic
Parametric Computation of the Legendre-Fenchel Conjugate with Application to the Computation of the Moreau Envelope
Journal of convex analysis, Tome 14 (2007) no. 3, pp. 657-666 Cet article a éte moissonné depuis la source Heldermann Verlag

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A new algorithm, named the Parametric Legendre Transform (PLT) algorithm, to compute the Legendre-Fenchel conjugate of a convex function of one variable is presented. It returns a parameterization of the graph of the conjugate except for some affine parts corresponding to nondifferentiable points of the function. The approach is extended to the computation of the Moreau envelope, resulting in a simple yet efficient algorithm.
Classification : 65Y20, 52A41, 90C25
Mots-clés : Legendre-Fenchel transform, Fenchel conjugate, Moreau envelope, Moreau-Yosida regularization, fast algorithm, computational convex analysis 
@article{JCA_2007_14_3_JCA_2007_14_3_a10,
     author = {J.-B. Hiriart-Urruty and Y. Lucet},
     title = {Parametric {Computation} of the {Legendre-Fenchel} {Conjugate} with {Application} to the {Computation} of the {Moreau} {Envelope}},
     journal = {Journal of convex analysis},
     pages = {657--666},
     year = {2007},
     volume = {14},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a10/}
}
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J.-B. Hiriart-Urruty; Y. Lucet. Parametric Computation of the Legendre-Fenchel Conjugate with Application to the Computation of the Moreau Envelope. Journal of convex analysis, Tome 14 (2007) no. 3, pp. 657-666. http://geodesic.mathdoc.fr/item/JCA_2007_14_3_JCA_2007_14_3_a10/