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References
H. Attouch. ‘Familles d'operateurs maximaux monotones et mesurabilité'. Ann. Mat. Pura Appl. 120 (1979), 35–111.
H. Attouch. ‘Variational convergence for functions and operators'. Applicable Mathematics Series. Pitman Advanced Publishing Program (1984).
H. Attouch. ‘Theorie de la Γ-convergence. Applications à des inéquations variationnelles de la mécanique'. Seminaire Goulaouic — Meyer-Schwartz (1982–83). Publications Ecole Polytechnique (Palaiseau).
H. Attouch. ‘Variational properties of epi-convergence'. Proceedings of the international congress on multifunctions and normal integrands, stochastic analysis, approximation and optimization'. Catane (Sicilia) (1984), G. Salinetti (ed.), Lecture Notes in Math, 1091 Springer Verlag, Berlin.
H. Attouch and R. Wets. ‘A convergence theory for saddle functions'. Trans. Amer. Math. Soc. Vol 280, n.1, Nov.(1983).
H. Attouch and R. Wets. ‘A convergence for bivariate functions aimed at the convergence of saddle value'. Proceedings S.Margherita Ligure on ‘Mathematical theories of optimization'. Edited by J.P.Cecconi and T. Zolezzi. Lecture Notes in Math. 979, Springer Verlag, (1981).
H. Attouch and R. Wets. ‘Isometries for the Legendre-Fenchel transform'. Publications Ceremade Paris-Dauphine (1984) (to appear).
H. Attouch and R. Wets. ‘Approximation and convergence in non linear optimization', in Nonlinear Programming 4, (Eds. O. Mangasarian, R. Meyer, S. Robinson) Academic Press, New York, 367–394, (1981).
D. Aze. ‘Epi-convergence et dualité. Application à la convergence des variables primales et duales pour des suites de problèmes en optimisation convexe'. Publication AVAMAC (Univ. Perpignan) 1984–85 (to appear).
D. Aze. ‘Deux exemples de convergence d'infima de problèmes d'optimisation sous leur forme duale par des méthodes d'epi-convergence'. Publication AVAMAC (Univ. Perpignan) 1984–85 (to appear).
H. Attouch, D. Aze and R. Wets. ‘Convergence of convex-concave saddle functions. Publication AVAMAC (Univ. Perpignan) 1984–85 (to appear).
T. Back. ‘Continuity of the Fenchel transform of convex functions'. Tech. Report, Northwestern University, Nov. 1983.
A.Bensoussan, J.L. Lions and G. Papanicolaou. ‘Asymptotic analysis for periodic structures'. North Holland (1978).
E. Cavazzuti. ‘Alcune caratterizzazioni della Γ-convergenza multipla'. Annali di Matematica pura ed applicata (1982) (IV), Vol. XXXII, pp. 69–112.
S. Dolecki. ‘Duality in optimization and continuity of polarities; International School of Math. "G. Stampacchia", Erice (1984).
E. De Giorgi. ‘Convergence problems for functionals and operators'. Proceedings of the international meeting on recent methods in nonlinear analysis. Rome, May(1978). Edited by E. De Giorgi, E. Magenés, U. Mosco. Pitagora. Editrice Bologna.
E. De Giorgi and T. Franzoni. ‘Su un tipo di convergenza variazionale'. Rend. Acc. Naz. Lincei, 58 (1975), 842–850.
E. De Giorgi and G. Dal Maso. ‘Γ-convergence and calculus of variations'. Proceedings S.Margherita Ligure (1981) ‘Mathematical Theories of Optimization'. Edited by J.P. Cecconi and T. Zolezzi. Lecture Notes in Math. 979, Springer Verlag.
E. De Giorgi and S. Spagnolo. ‘Sulla convergenza degli integrali dell'energia per operatori ellittici del II ordine'. Boll. Un. Mat. Ital. (4) 8, 391–411 (1973).
I. Ekeland and R. Temam. ‘Convex analysis and variational problems'. North Holland (1978).
J.L. Joly. ‘Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarité est bicontinue'. J. Math. Pures Appl., 52, 421–441 (1973).
J.L. Lions. 'some methods in the Mathematical analysis of systems and their control'. Science Press, Pekin, China. Gordon and Breach, Science Publishers, Inc. New York.
R. Lucchetti and F. Patrone. ‘Closure and upper semicontinuity results in mathematical programming'. Nash and economic equilibria (to appear).
L. Mac Linden. ‘Successive approximation and linear stability involving convergent sequences of optimization problems'. J. of Approximation theory 35, 311–354 (1982).
L. Mac Linden and R.C. Bergstrom. ‘Preservation of convergence of convex sets and functions in finite dimensions'. Transactions of the American Math. Soc. Vol. 268, n.1, (1981).
P. Marcellini. ‘Periodic solutions and homogenization of non linear variational problems'. Ann. Mat. Pura. Appl. (4), 117, 139–152 (1978).
U. Mosco. ‘Convergence of convex sets and of solutions of variational inequalities'. Advances in Math., 3, 510–585 (1969).
U. Mosco. ‘On the continuity of the Young-Fenchel transformation'. J. Math. Anal. Appl. 35, 518–535 (1971).
N. Papageorgiou. 'stochastic nonsmooth analysis and optimization'. Thesis University of Illinois.
R.T. Rockafellar. ‘A general correspondance between dual minimax problems and convex programs'. Pacific J. Math., 25, 597–611 (1968).
Y. Sonntag. ‘Convergence au sens de Mosco'...Thèse d'état. Université de Provence (Marseille) (1982).
P. Suquet. ‘Plasticité et homogénéisation'. Thèse d'état. Paris (1982).
M. Volle. ‘Conjugaison par tranches'. Ann. Mat. Pura Appl. (4), 139, 279–311, (1985).
D. Walkup and R. Wets. ‘Continuity of some convex-cone valued mappings'. Proceed. Amer. Math. Soc. 18 (1967), 229–235.
R. Wets. ‘Convergence of convex functions, variational inequalities and convex optimization problems in Variational Inequalities and Complementarity problems'. Eds. P. Cottle, F. Giannessi, J.L. Lions, Wiley, Chichester (UK) 375–403 (1980).
R. Wets. ‘A formula for the level sets of epi-limits and some applications'. Working paper, I.I.A.S.A. (Laxenburg, Austria) Sept. 1982.
R. Wijsman. ‘Convergence of sequences of convex sets, cones and functions II. Transactions Amer. Math. Soc. 123, 32–45 (1966).
T. Zolezzi. ‘On stability analysis in mathematical programming'. Mathematical Programming studies. Fiacco editor, (to appear).
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Attouch, H. (1986). Epi-convergence and duality. Convergence of sequences of marginal and lagrangians functions. Applications to homogenization problems in mechanics. In: Conti, R., De Giorgi, E., Giannessi, F. (eds) Optimization and Related Fields. Lecture Notes in Mathematics, vol 1190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076701
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