Moreau's decomposition theorem revisited

J. B. Hiriart-Urruty; Ph. Plazanet

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: S6, page 325-338
  • ISSN: 0294-1449

How to cite

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Hiriart-Urruty, J. B., and Plazanet, Ph.. "Moreau's decomposition theorem revisited." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 325-338. <http://eudml.org/doc/78201>.

@article{Hiriart1989,
author = {Hiriart-Urruty, J. B., Plazanet, Ph.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hilbert space; lower-semicontinuous convex function; deconvolution},
language = {eng},
pages = {325-338},
publisher = {Gauthier-Villars},
title = {Moreau's decomposition theorem revisited},
url = {http://eudml.org/doc/78201},
volume = {S6},
year = {1989},
}

TY - JOUR
AU - Hiriart-Urruty, J. B.
AU - Plazanet, Ph.
TI - Moreau's decomposition theorem revisited
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 325
EP - 338
LA - eng
KW - Hilbert space; lower-semicontinuous convex function; deconvolution
UR - http://eudml.org/doc/78201
ER -

References

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  1. 1 - E. Asplund, Differentiability of the metric projection in finite-dimensional Euclidean space, Proceedings of the Amer. Math. Society38 (1973), 218-219. Zbl0269.52002MR310150
  2. 2 - D. Aze and J-P. Penot, Uniformly convex functions and uniformly smooth convex functions, preprint (1987). Zbl0870.49010
  3. 3 - J-B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, in Convexity and Duality in Optimization, Lecture Notes in Economics and Mathematical Systems256 (1986), 37-70. Zbl0591.90073MR873269
  4. 4 - J-B. Hiriart-Urruty and M-L. Mazure, Formulations variationnelles de l'addition parallèle et de la soustraction parallèle d'opérateurs semi-définis positifs, C.R. Acad. Sc. Paris, 1. 302, Série I, n° 15 (1986), 527-530. Zbl0597.15008MR845640
  5. 5 - J-B. Hiriart-Urruty, A general formula on the conjugate of the difference of functions, Canad. Math. Bull., Vol 29 (4) (1986), 482-485. Zbl0608.90087MR860858
  6. 6 - J-M. Lasry and P.-L. Lions, A remark on regularization in Hilbert spaces, Israel J. of Mathematics55 (1986), 257-266. Zbl0631.49018MR876394
  7. 7 - J-J. Moreau, Décomposition orthogonale d'un espace hilbertien selon deux cônes mutuellement polaires, C.R. Acad. Sc., t.255 (1962), 238-240. Zbl0109.08105MR139919
  8. 8 - J-J. Moreau, Proximité et dualité dans un espace Hilbertien, Bull. Soc. Math. France93 (1965), 273-299. Zbl0136.12101MR201952
  9. 9 - J-J. Moreau, Weak and strong solutions of dual Problems in Contributions to Nonlinear Functional Analysis (E. Zarantonello, Editor), Academic Press (1971). Zbl0274.49007MR410505
  10. 10 - M. Volle, private communication (June 1987). 
  11. 11 - A.P. Wierzbicki and S. Kurcyuz, Projection on a cone, penalty functionals and duality theory for problems with inequality contraints in Hilbert space, SIAM J. Control and Optimization15 (1977), 25–26. Zbl0355.90045MR438720

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