References
Aze D., Volle M. Various continuity properties of the deconvolution // Lect. Notes in Econ. and Math. Systems. —1991. — 382. — P. 16–30.
Hiriart-Urruty J.-B. A general formula on the conjugate of the difference of functions // Canadian Math. Bulletin. — 1986 — 29, No. 4. — P. 482–485.
Hiriart-Urruty J.-B., Mazure M.-L. Formulations variationnelles de l'addition parallele et de la soustraction parallele d'operateurs semi-definis positifs // Note aux C.R. Acad. Sci. Paris. — 1986. — 302. — P. 527–530.
Hiriart-Urruty J.-B. How to regularize a difference of convex functions // J. of Math. Analysis and Applications. — 1991. — 162. — P. 196–209.
Hiriart-Urruty J.-B., Lemarechal C. Convex Analysis and Minimization Algorithms // Grundlehren der mathematischen Wissenschaften. — 1993. — Springer Verlag, 305, 306.
Martinez-Legaz J.E., Seeger A., A formula on the approximate subdifferential of the difference of convex functions // Bull. Austral. Math. Soc. — 1992. — 45. — P. 37–41.
Mazure M.-L. La soustraction parallele d'operateurs interpretee comme deconvolution de formes quadratiques convexes // Optimization. — 1987. — 18. — P. 465–484.
Mazure M.-L. Equations de convolution et formes quadratiques // Ann. di Mat. Pura. Appl. 1991. — 158. — P. 75–97.
Mazure, M.-L., Volle M. Equations inf-convolutives et conjugaison de Moreau-Fenchel // Ann. de la Faculte des Sciences de Toulouse. — 1991. — 12. — P. 103–126.
Pekarev E.L., Smul'jan L. Parallel addition and parallel subtraction of operators // Math. USSR Izvestija. —1976. — 10. — P. 351–370.
Pshenichnyi B.N. Lecons sur les jeux differentiels // Controle Optimal et Jeux Differentiels. — 1971. — Cahier N. 4 de l'I.R.I.A.
Rokafellar R.T. Convex Analysis 1970, Princeton University Press.
Volle M. A formula on the subdifferential of the deconvolution of convex functions // Bull. Austral. Math. Soc.— 1993. — 47. — P. 333–340.
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Published in Kibernetika i Sistemnyi Analiz, Vol. 30, No. 4, pp. 97–104, July–August, 1994.
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Hiriart-Urruty, J.B. The deconvolution operation in convex analysis: An introduction. Cybern Syst Anal 30, 555–560 (1994). https://doi.org/10.1007/BF02366565
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DOI: https://doi.org/10.1007/BF02366565