Free Access
Volume 9, February 2003
Page(s) 297 - 315
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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.