Uniformly convex and uniformly smooth convex functions

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1. [1] Asplund ( E.) .— Fréchet Differentiability of convex functions, Acta Matematica121 (1967), pp. 31-47. Zbl0162.17501MR231199
2. [2] Asplund ( E.) .— Positivity of duality mappings, Bull. Am. Math. Soc.73 (1967), pp. 200-203. Zbl0149.36202MR206663
3. [3] Asplund ( E.) and Rockafellar ( R.T.) .— Gradients of convex functions, Trans. Am. Math. Soc.139 (1969), pp. 443-467. Zbl0181.41901MR240621
4. [4] Attouch ( H.) and Wets ( R.J.-B.) .— A quantitative approach via epigraphic distances to stability of strong local minimizers, Technical report No 87-01, Univ. of Perpignan (1987). 
5. [5] Aubin ( J.-P.) and Ekeland ( I.) .— Nonlinear applied analysis, J. Wiley, New York (1984). Zbl0641.47066MR749753
6. [6] Auslender ( A.) .— Optimisation — Méthodes numériques, Masson, Paris (1976). Zbl0326.90057MR441204
7. [7] Beauzamy ( B.) .— Introduction to Banach spaces and their geometry, Mathematical Studies68, North-Holland, Amsterdam (1982). Zbl0491.46014MR670943
8. [8] Bishop ( E.) and Phelps ( R.R.) .— The support functionals of a convex set, In Convexity edited by P. Klee, Proc. Symp. Pure Math.7, Am. Math. Soc.Providence (1963), pp. 27-35. Zbl0149.08601MR154092
9. [9] Bröndsted ( A.) and Rockafellar ( R.T.) .— On the subdifferentiability of convex functions, Proc. Am. Math. Soc.16 (1965), pp. 605-611. Zbl0141.11801MR178103
10. [10] Browder ( F.E.) .— Problèmes non linéaires, Presses de l'Université de Montréal15 (1966). Zbl0153.17302
11. [11] Bynum ( J.C.) .— Characterizations of uniform convexity, Pac. J. Math.38, No 3 (1971), pp. 577-581. Zbl0229.46019MR305034
12. [12] Ciarlet ( P.G.) .- Introduction à l'analyse numérique matricielle et à l'optimisation, Masson, Paris (1982). Zbl0488.65001MR680778
13. [13] Cioranescu ( I.) .— Duality mappings in the nonlinear functional analysis, Ed. Acad. R.S.R., Bucharest (1974) (in Romanian). MR383157
14. [14] Diestel ( J.) .— Geometry of Banach spaces, selected topics, Lecture Notes in Mathematics485, Springer, Berlin (1975). Zbl0307.46009MR461094
15. [15] Donchev ( A.L.) .— Perturbations, approximations and sensitivity analysis of optimal control systems, SpringerLecture Notes in Control52 (1984). Zbl0512.49001MR790847
16. [16] Dunn ( J.C.) .— Convexity, monotonicity and gradient processes in Hilbert spaces, J. Math. Anal. Appl.53 (1976), pp. 145-158. Zbl0321.49025MR388176
17. [17] Ekeland ( I.) .— Two results in convex analysis, in "Optimization and related fields", Ed. by R. Conti, E. de Giorgi and F. Giannessi, Lecture Notes in Mathematics1190, SpringerBerlin (1986). Zbl0589.49007MR858352
18. [18] Figiel ( T.) .— On the moduli of convexity and smoothness, Stud. Math.56 (1976), pp. 121-155. Zbl0344.46052MR425581
19. [19] Jeyakumar ( V.) . — On subgradient duality with strong and weak convex functions, J. Austr. Math. Soc.40, Ser. A (1986), 143-152. Zbl0598.90094MR817834
20. [20] Jeyakumar ( V.) . — p-convexity and second order duality, Util. Math.29 (1986), pp. 71-85. Zbl0557.90080MR846192
21. [21] Karmanov ( V.) .— Programmation Mathématique, French translation, Mir, Moscow (1975). Zbl0379.90068
22. [22] Levitin ( E.) and Poljak ( B.), .— Minimization methods in the presence of constraints, Z. Vycisl. Mat. i. Fiz.6, No 5 (1966), pp. 787-823. Zbl0184.38902MR211590
23. [23] Levitin ( E.) and Poljak ( B.) .— Convergence of minimizing sequences in conditional extremum problems, Sov. Math. Dokl.7 (1967), pp. 764-767. Zbl0161.07002MR199016
24. [24] Lucchetti ( R.) and Patrone ( F.) .— Hadamard and Tyhonov well-posedness of a certain class of convex functions, J. Math. Anal. Appl.88 (1982), pp. 204-215. Zbl0487.49013MR661413
25. [25] Lyubich ( Y.) and Maistrovski ( G.) .— The general theory of relaxation processes for convex functionals, Russ. Math. Surv.25 (1970), pp. 57-117. Zbl0207.45001
26. [26] Milman ( V.D.) .— A certain transformation of convex functions and a duality of the β and δ characteristics of a β space, Dokl. Akad. Nauk. SSSR187 (1969), pp. 33-45. Zbl0188.43503MR256138
27. [27] Psenitchny ( B.) and Daniline ( Y.) .— Méthodes numériques dans les problèmes d'extremum, French translation, Mir, Moskow (1975). 
28. [28] Penot ( J.-P.) .— Metric regularity, openness and Lipschitzian behaviour of multifunctions, Nonlinear Anal. Theory Methods Appl.13, No 6 (1989), pp. 629-643. Zbl0687.54015MR998509
29. [29] Penot ( J.-P.) and Volle ( V.) .— Inversion of real valued functions and applications, Z.O.R. Methods and Models of Operations Research34 (1990), pp. 117-141. Zbl0718.49012MR1045821
30. [30] Penot ( J.-P.) and Volle ( M.) .— On strongly convex and paraconvex dualities, in "Generalized Convexity and Fractional Programming with Economics Applications", Proc. Pisa. Italy (1988), A. Cambini et al. Eds. Lecture Notes in Economics and Mathematical Systems345, Springer VerlagBerlin (1990), pp. 198-218. Zbl0701.49038MR1117933
31. [31] Poljak ( B.) . — Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Sov. Math. Dokl.7 (1967), pp. 72-75. Zbl0171.09501MR198307
32. [32] Prüss ( J.) . — A Characterization of uniform convexity and application to accretive operators, Hiroshima Math. J.11 (1981), pp. 229-234. Zbl0464.47035MR620534
33. [33] Roberts ( A.W.) and Varberg ( D.) .— Convex functions, Academic Press, New York (1973). Zbl0271.26009MR442824
34. [34] Rockafellar ( R.T.) .- Monotone operators and the proximal point algorithm, SIAM J. Control Opt.14 (1976), pp. 877-898. Zbl0358.90053MR410483
35. [35] Šmulyan ( V.L.) .— Sur la dérivabilité de la norme dans l'espace de Banach, Dokl. Acad. Naukl. SSSR, 27 (1940), pp. 643-648. Zbl0023.32604MR2704
36. [36] Vial ( J.P.) .— Strong convexity of sets and functions, J. Math. Econ.9 (1982) pp. 187-205. Zbl0479.52005MR637263
37. [37] Vial ( J.-P.) .— Strong and weak convexity of sets and functions, Math. Oper. Res.8 (1983), pp. 231-259. Zbl0526.90077MR707055
38. [38] Vladimirov ( A.A.), Nesterov ( Yu E.) and Chekanov ( Yu N.) .— On uniformly convex functionals, Vest. Mosk. Univ.3, Ser. XV (1978), pp. 12-23. Zbl0442.47046MR516874
39. [39] Vladimirov ( A.A.), Nesterov ( Yu E.) and Chekanov ( Yu N.) .— On uniformly quasi-convex functionals, Vest. Mosk. Univ.4, Ser. XV (1978), pp. 18-27. Zbl0453.47047MR525130
40. [40] Volle ( M.) Personal communication. 
41. [41] Zalinescu ( C.) .— On uniformly convex functions, J. Math. Anal. Appl.95 (1983), pp. 344-374. Zbl0519.49010MR716088
42. [42] Zolezzi ( T.) .— On equiwellset minimum problems, Appl. Math. Optimization4 (1978), pp. 209-223. Zbl0381.90105MR493627