Free Access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 297 - 315
DOI https://doi.org/10.1051/cocv:2003014
Published online 15 September 2003
  1. H. Attouch, Variational convergence for functions and operators. Pitman, London, Appl. Math. Ser. (1984). [Google Scholar]
  2. H. Attouch et D. Aze, Regularization and approximation of sets and functions in Hilbert spaces, dans Séminaire d'Analyse Numérique, Paper XI. Université Paul Sabatier de Toulouse (1987-1988). [Google Scholar]
  3. H. Attouch, D. Aze et R.J.-B. Wets, Convergence of convex-concave saddle functions : Continuity properties of the Legendre-Fenchel transform and applications to convex programming. Ann. Inst. H. Poincaré Anal. Non linéaire 5 (1988) 537-572. [Google Scholar]
  4. H. Attouch et G. Beer, On the convergence of subdifferentials of convex functions. Arch. Math. 60 (1993) 389-400. [CrossRef] [MathSciNet] [Google Scholar]
  5. H. Attouch et H. Brezis, Duality for the sum of convex functions in general Banach spaces, Publications AVAMAC. Université de Perpignan, Nos. 84-10. Av. (1984). [Google Scholar]
  6. H. Attouch et R.J.-B. Wets, Quantitative stability of variational systems: I. The epigraphical distance. Trans. Amer. Math. Soc. 328 (1991) 695-729. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Attouch et R.J.-B. Wets, Quantitative stability of variational systems: II. A framework for nonlinear conditionning, IIASA working paper 88-9. Laxemburg, Austria (1988). [Google Scholar]
  8. H. Attouch et R.J.-B. Wets, Quantitative stability of variational systems: III. Stability of minimizers, Working paper IIASA. Laxemburg, Austria (1988). [Google Scholar]
  9. H. Attouch et R.J.-B. Wets, A quantitative approach via epigraphic distance to stability of strong local minimizers, Publications AVAMAC. Université de Perpignan (1987). [Google Scholar]
  10. D. Aze, Convergences variationnelles et dualité. Applications en calcul des variations et en programmation mathématique, Thèse de Doctorat d'État. Université de Perpignan (1986). [Google Scholar]
  11. D. Aze et J.-P. Penot, Operations on convergent families of sets and functions. Optim. 21 (1990) 521-534. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Bank, J. Guddat, D. Klatte, B. Kummer et K. Tammer, Nonlinear parametric optimization. Akademie Verlag (1982). [Google Scholar]
  13. G. Beer, On Mosco convergence of convex sets. Bull. Austral. Math. Soc. 38 (1988) 239-253. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Beer, Conjugate convex functions and the epi-distance topology. Proc. Amer. Math. Soc. 108 (1990) 117-126. [MathSciNet] [Google Scholar]
  15. G. Beer, The slice topology: A viable alternative to Mosco convergence in nonreflexive spaces. Nonlinear. Anal. Theo. Meth. Appl. 19 (1992) 271-290. [CrossRef] [Google Scholar]
  16. G. Beer et R. Lucchetti, Convex optimization and the epi-distance topology. Trans. Amer. Math. Soc. 327 (1991) 795-813. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Beer et R. Lucchetti, The epi-distance topology: Continuity and stability results with applications to convex optimization problems. Math. Oper. Res. 17 (1992) 715-726. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Beer et M. Thera, Attouch-Wets convergence and a differential operator for convex functions. Proc. Amer. Math. Soc. 122 (1994) 851-858. [MathSciNet] [Google Scholar]
  19. N. Bourbaki, Espaces vectoriels topologiques, Chaps. 1-2. Hermann, Paris (1966). [Google Scholar]
  20. D.L. Burkholder et R.A. Wijsman, Optimum properties and admissibility of sequentiel tests. Ann. Math. Statist. 34 (1963) 1-17. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. Castaing et M. Valadier, Convex analysis and measurable multifunctions. Springer, Lecture Notes in Math. 580 (1977). [Google Scholar]
  22. J. Dieudonne, Sur la séparation des ensembles convexes. Math. Annal. 163 (1966) 1-3. [CrossRef] [Google Scholar]
  23. A.L. Dontchev et T. Zolezzi, Well-posed optimization problems. Springer-Verlag, Berlin, Lecture Notes in Math. 1543 (1993). [Google Scholar]
  24. I. Ekeland et R. Temam, Analyse convexe et problèmes variationnels. Dunod, Paris (1974). [Google Scholar]
  25. K. El Hajioui, Convergences variationnelles : approximations inf-convolutives généralisées, stabilité et optimisation dans les espaces non réflexifs, Thèse Nationale. Kénitra (2002). [Google Scholar]
  26. K. El Hajioui et D. Mentagui, Slice convergence : stabilité et optimisation dans les espaces non réflexifs. Preprint. [Google Scholar]
  27. J. Garsoux, Espaces vectoriels topologiques et distributions. Dunod, Paris (1963). [Google Scholar]
  28. J.L. Joly, Une famille de topologies et de convergences sur l'ensemble des fonctionnelles convexes, Thèse d'État. Grenoble (1970). [Google Scholar]
  29. K. Kuratowski, Topology, Vol. I. Academic Press, New York (1966). [Google Scholar]
  30. P.J. Laurent, Approximation et optimisation. Hermann (1972). [Google Scholar]
  31. L. McLinden et R. Bergstrom, Preservation of convergence of convex sets and functions in finite dimensions. Trans. Amer. Math. Soc. 268 (1981) 127-142. [CrossRef] [MathSciNet] [Google Scholar]
  32. D. Mentagui, Stability results of a class of well-posed optimization problems. Optim. 36 (1996) 119-138. [CrossRef] [Google Scholar]
  33. D. Mentagui, Stabilité de l'épi-convergence en dimension finie. Pub. Inst. Math. 59 (1996) 161-168. [Google Scholar]
  34. D. Mentagui et K. El Hajioui, Convergences des fonctions convexes et approximations inf-convolutives généralisées. Pub. Inst. Math. (à paraître). [Google Scholar]
  35. J.J. Moreau, Proximité et dualité dans un espace Hilbertien. Bull. Soc. Math. France 93 (1965) 273-299. [CrossRef] [MathSciNet] [Google Scholar]
  36. U. Mosco, Approximation of the solutions of some variational inequalities. Ann. Scuola Normale Sup. Pisa 21 (1967) 373-394. [Google Scholar]
  37. U. Mosco, Convergence of convex sets and of solutions of variational inequalities. Adv. in Math. 3 (1969) 510-585. [CrossRef] [Google Scholar]
  38. U. Mosco, On the continuity of the Young-Fenchel transform. J. Math. Anal. Appl. 35 (1971) 518-535. [CrossRef] [MathSciNet] [Google Scholar]
  39. R. Robert, Convergences de fonctionnelles convexes. J. Math. Anal. Appl. 45 (1974) 533-555. [CrossRef] [MathSciNet] [Google Scholar]
  40. R.T. Rockafellar, Convex Analysis. Princeton University Press (1970). [Google Scholar]
  41. R.T. Rockafellar, Level sets and continuity of conjugate convex functions. Trans. Amer. Math. Soc. 123 (1966) 46-63. [CrossRef] [MathSciNet] [Google Scholar]
  42. R.T. Rockafellar et R.J.-B. Wets, Variational analysis. Springer (1998). [Google Scholar]
  43. G. Salinetti et R.J.-B. Wets, On the relations between two types of convergence for convex functions. J. Math. Anal. Appl. 60 (1977) 211-226. [CrossRef] [MathSciNet] [Google Scholar]
  44. Y. Sonntag, Convergence au sens de Mosco : théorie et applications à l'approximation des solutions d'inéquations, Thèse d'État. Université de Provence, Marseille (1982). [Google Scholar]
  45. Y. Sonntag et C. Zalinescu, Set convergences: An attempt of classification. Trans. Amer. Math. Soc. 340 (1993) 199-226. [CrossRef] [MathSciNet] [Google Scholar]
  46. B. Van Cutsem, Problems of convergence in stochastic linear programming, dans Techniques of optimization, édité parBalakrishnan. Academic Press, New York (1972) 445-454. [Google Scholar]
  47. R.J.-B. Wets, A formula for the level sets of epi-limits and some applications. Mathematical theories of optimization, édité par J.P. Cecconi et T. Zolezzi. Springer, Lecture Notes in Math. 983 (1983). [Google Scholar]
  48. R.A. Wijsman, Convergence of sequences of convex sets, cones and functions. Bull. Amer. Math. Soc. 70 (1964) 186-188. [CrossRef] [MathSciNet] [Google Scholar]
  49. R.A. Wijsman, Convergence of sequences of convex sets, cones and functions II. Trans. Amer. Math. Soc. 123 (1966) 32-45. [CrossRef] [MathSciNet] [Google Scholar]

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