116
CHAPITRE 4. ANALYSE CONVEXE OPÉRATOIRE
Références
[A] D. Azé. Éléments d’analyse convexe. Éditions Ellipses, Paris, 1997.
[ET] I. Ekeland and R. Temam. Convex analysis and variational problems.
Reprinted by SIAM Publications, Classics in, Applied Mathematics,
28, 1999.
[HU1] J.-B. Hiriart-Urruty. "Lipschitz r-continuity of the approximate subdifferential of a convex function". Math. Scan. 47 (1980), p. 123–134.
[HUL] J.-B. Hiriart-Urruty and C. Lemaréchal. Convex analysis and minimization algorithms. Grundlehren der mathematischen Wissenschaften,
Vol. 305 and 306, Springer Verlag, Berlin Heidelberg, 1993. Second
printing in 1996.
[HU2] J.-B. Hiriart-Urruty and Ph. Plazanet. "Moreau’s decomposition revisited". Annales de l’Institut Henri Poincaré : Analyse non linéaire,
supplément au Vol. 6 (1989), p. 325–338.
[HU3] J.-B. Hiriart-Urruty. "From convex optimization to nonconvex optimization. Part I : Necessary and sufficient conditions for global optimality". Nonsmooth optimization and related topics, Ettore Majorana
International Science Series, 43 (1989), Plenum Press, p. 219–239.
[HU4] J.-B. Hiriart-Urruty. "The deconvolution operation in convex analysis : an introduction". Cybernetics and systems analysis, 4 (1994), p.
97–104.
[R] R.T. Rockafellar. Convex Analysis. Princeton University Press, 1970.
[Z] C. Zalinescu. Convex Analysis in General Vector Spaces. World Scientific, Singapore, 2002.
[M] J.-J. Moreau. "Proximité et dualité dans un espace hilbertien". Bull. Soc.
Math. France, 93 (1965), p. 273–299.
[CP] P. L. Combettes and J.-C. Pesquet. "Proximal thresholding algorithm
for minimization over orthonormal bases". SIAM J. Optimization Vol.
18, 4 (2007), p. 1351–1376.
[AM] S. Artstein-Avidan and V. Milman. "The concept of duality in convex
analysis, and the characterization of the Legendre transform". Annals
of Mathematics, 169 (2009), p. 661–674.
CHAPITRE 4. ANALYSE CONVEXE OPÉRATOIRE
Références
[A] D. Azé. Éléments d’analyse convexe. Éditions Ellipses, Paris, 1997.
[ET] I. Ekeland and R. Temam. Convex analysis and variational problems.
Reprinted by SIAM Publications, Classics in, Applied Mathematics,
28, 1999.
[HU1] J.-B. Hiriart-Urruty. "Lipschitz r-continuity of the approximate subdifferential of a convex function". Math. Scan. 47 (1980), p. 123–134.
[HUL] J.-B. Hiriart-Urruty and C. Lemaréchal. Convex analysis and minimization algorithms. Grundlehren der mathematischen Wissenschaften,
Vol. 305 and 306, Springer Verlag, Berlin Heidelberg, 1993. Second
printing in 1996.
[HU2] J.-B. Hiriart-Urruty and Ph. Plazanet. "Moreau’s decomposition revisited". Annales de l’Institut Henri Poincaré : Analyse non linéaire,
supplément au Vol. 6 (1989), p. 325–338.
[HU3] J.-B. Hiriart-Urruty. "From convex optimization to nonconvex optimization. Part I : Necessary and sufficient conditions for global optimality". Nonsmooth optimization and related topics, Ettore Majorana
International Science Series, 43 (1989), Plenum Press, p. 219–239.
[HU4] J.-B. Hiriart-Urruty. "The deconvolution operation in convex analysis : an introduction". Cybernetics and systems analysis, 4 (1994), p.
97–104.
[R] R.T. Rockafellar. Convex Analysis. Princeton University Press, 1970.
[Z] C. Zalinescu. Convex Analysis in General Vector Spaces. World Scientific, Singapore, 2002.
[M] J.-J. Moreau. "Proximité et dualité dans un espace hilbertien". Bull. Soc.
Math. France, 93 (1965), p. 273–299.
[CP] P. L. Combettes and J.-C. Pesquet. "Proximal thresholding algorithm
for minimization over orthonormal bases". SIAM J. Optimization Vol.
18, 4 (2007), p. 1351–1376.
[AM] S. Artstein-Avidan and V. Milman. "The concept of duality in convex
analysis, and the characterization of the Legendre transform". Annals
of Mathematics, 169 (2009), p. 661–674.