Convergence of convex-concave saddle functions : applications to convex programming and mechanics
Annales de l'I.H.P. Analyse non linéaire, Volume 5 (1988) no. 6, pp. 537-572.
corrected-by Erratum
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     title = {Convergence of convex-concave saddle functions : applications to convex programming and mechanics},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {537--572},
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     year = {1988},
     mrnumber = {978671},
     zbl = {0667.49009},
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     url = {http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/}
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Azé, Dominique; Attouch, Hedy; Wets, Roger J.-B. Convergence of convex-concave saddle functions : applications to convex programming and mechanics. Annales de l'I.H.P. Analyse non linéaire, Volume 5 (1988) no. 6, pp. 537-572. http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/

[1] R. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc., Vol. 123, 1966, pp. 32-45. | MR | Zbl

[2] U. Mosco, Convergence of Convex Sets and Solutions of Variational Inequalities, Advances Math., Vol. 3, 1969, pp. 510-585. | MR | Zbl

[3] E. De Giorgi, Convergence Problems for Functionals and Operators, Proceed. on Recent Methods in Non-linear Analysis, E. DE GIORGI, E. MAGENES and U. Mosco Eds., Pitagora Editrice, Bologna, 1980.

[4] H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series, Pitman, London, 1984. | MR | Zbl

[5] U. Mosco, On the Continuity of the Young-Fenchel Transform, J. Math. Anal. Appl., Vol. 35, 1971, pp. 518-535. | MR | Zbl

[6] J.-L. Joly, Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarité est bicontinue, J. Math. Pures Appl., Vol. 52, 1973, pp. 421-441. | MR | Zbl

[7] K. Back, Continuity of the Fenchel Transform of Convex Functions, Proceedings of the American Mathematical Society, Vol. 97, 1986, pp. 661-667. | MR | Zbl

[8] R.T. Rockafellar, A General Correspondence Between Dual Minimax Problems and Convex Programs, Pacific J. Math., Vol. 25, 1968, pp. 597-611. | MR | Zbl

[9] I. Ekeland and R. Teman, Convex Analysis and Variational Problems, North Holland, Amsterdam, 1978.

[10] H. Attouch and R. Wets, A Convergence Theory for Saddle Functions, Trans. Amer. Math. Soc., Vol. 280, 1983, pp. 1-44. | MR | Zbl

[11] H. Attouch and R. Wets, A Convergence for Bivariate functions aimed at the Convergence of Saddle Values, in Mathematical Theories of Optimization, J. CECCONI and T. ZOLEZZI Eds., Springer-Verlag Lecture Notes in Mathematics, No. 979, 1981, pp. 1-42. | MR | Zbl

[12] E. Cavazutti, Alcune caratterizzazioni della Γ-convergenza multipla, Annali Mat. Pura Applicata, Vol. 32, 1982, pp. 69-112.

[13] E. Cavazutti, Γ-convergenza multipla, convergenza di punti di sella e di max-min, Boll. Un. Mat. Ital., (6), Vol. 1-B, 1982, pp. 251-274.

[14] G. Greco, Saddle Topology and Min-Max Theorems, Tech. Report. Univ. Trento., 1984.

[15] Y. Sonntag, Convergence au sens de Mosco; théorie et applications à l'approximation des solutions d'inéquations, Thèse d'État, Marseille, 1982.

[16] A. Fougeres and A. Truffert, Régularisation s.c.i. et Γ-convergence, approximations inf-convolutives associées à un référentiel, Annali di Mat. Pura e appl., 1986 (to appear). | Zbl

[17] R.T. Rockafellar, Monotone operators Associated with Saddle Functions and Minimax Problems, in Nonlinear Functional Analysis, American Mathematical Society, Rhode Island, 1970. | MR | Zbl

[18] R.T. Rockafellar, Minimax Theorems and Conjugate Saddle Functions, Matematica Scandinavica, Vol. 14, 1964, pp. 151-173. | MR | Zbl

[19] L. Mclinden, An Extension of Fenchel Duality Theorem to Saddle Functions and Dual Minimax Problems, Pacific J. Mathematics, Vol. 50, 1974, pp. 135-158. | MR | Zbl

[20] L. Mclinden, Dual Operations on Saddle Functions, Trans. Amer. Math. Soc., Vol. 179, 1973, pp. 363-381. | MR | Zbl

[21] J.-P. Aubin, L'Analyse Non Linéaire et ses Motivations Économiques, Masson, 1984. | MR | Zbl

[22] R.T. Rockafellar, Conjugate Duality and Optimization, Regional Conference Series in Applied Mathematics, 16, S.I.A.M., Philadelphia, 1974. | MR | Zbl

[23] S. Robinson, Local Structure of Feasible Sets in Nonlinear Programming, part III: Stability and Sensitivity, Mathematical Programming Study, Vol. 22, 1984, pp. 217-230. | MR | Zbl

[24] A. Fiacco, Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, 1983. | MR | Zbl

[25] L. Mclinden and R. Bergstrom, Preservation of Convergence of Convex Sets and Functions in Finite Dimensions, Trans. Amer. Math. Soc., Vol. 268, 1981. | MR | Zbl

[26] J.-J. Moreau, Fonctionnelles convexes, séminaire équations aux dérivées partielles, Collège de France, Paris, 1966.

[27] J.-L. Joly, Une famille de topologies et de convergences sur l'ensemble des fonctionnelles convexes, Thèse d'état, Grenoble, 1970.

[28] J.-P. Aubin, Mathematical Methods of Game and Economic Theory, North Holland, 1979. | MR | Zbl

[29] T. Zolezzi, On Stability Analysis in Mathematical Programming, Mathematical Programming study, Vol. 21, 1984, pp. 227-242. | MR

[30] L. Mclinden, Successive Approximation and Linear Stability Involving Convergent Sequences of Optimization Problems, J. Approximation Theory, Vol. 35, 1982, pp. 311-354. | MR | Zbl

[31] R. Lucchetti and F. Patrone, Closure and Upper Semicontinuity in Mathematical Programming, Nash and economic equilibria, Tech. Report, Univ. Genova, 1984.

[32] D. Azé, Stability Results in Convex Programming, Technical Report 85-04, A.V.A.M.A.C., Perpignan, 1985.

[33] A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR | Zbl

[34] L. Tartar, Cours Peccot au collège de France, Paris, 1977.

[35] E. De Giorgi and T. Franzoni, Su un tipo di convergenza variationale, Atti. Accad. Naz. Lincei, Rend. de sc. Mat., (8), Vol. 58, 1975, pp. 842-850. | MR | Zbl

[36] P. Marcellini, Periodic Solutions and Homogenization of Non Linear Variational Problems, Ann. Mat. Pura Appl., Vol. 117, 1978, pp. 139-159. | MR | Zbl

[37] A.V. Marchenko and E. Ya Hruslov, Boundary value problems in domains with close-grained Boundaries (Russian), Naukova Dumka, Kiev, 1974.

[38] H. Attouch, Variational Properties of Epi-Convergence, in Multifunctions and Integrands : Stochastic Analysis, Approximation and Optimization, G. SALINETTI Ed.; Springer-Verlag Lecture Notes in Mathematics, No. 1091, 1983.

[39] P. Suquet, Plasticité et homogénéisation, Thèse d'état, Paris-VI, 1982.

[40] D. Azé, Epi-convergence et dualité, applications à la convergence des variables duales pour des suites de problèmes d'optimisation convexe, Technical Report 84-12, A.V.A.M.A.C. Perpignan, 1984.

[41] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, 1972. | MR | Zbl

[42] A. Auslender, Optimisation: Méthodes numériques, Masson, 1976. | MR | Zbl

[43] D. Azé, Convergence des variables duales dans des problèmes de transmission à travers des couches minces par des méthodes d'épi-convergence, Ricerche di Matematica, vol. 35, 1986, pp. 125-159. | MR | Zbl

[44] H. Attouch, On the Maximality of the Sum of Two Maximal Monotone Operators, Nonlinear Analysis, Theory, Methods and Applications, Vol. 5, No. 2, 1981, pp. 143-147. | MR | Zbl

[45] F. Murat, H-Convergence, Rapport du séminaire d'analyse fonctionnelle et numérique, Université d'Alger, 1978.

[46] H. Attouch, Convergence de fonctionnelles convexes, Proc. journées d'analyse non linéaire, Besançon, 1977; Springer-Verlag Lecture Notes in Mathematics, No. 655, 1978, pp. 1-40. | MR | Zbl

[47] H. Attouch and R. Wets, Approximation and Convergence in Nonlinear Optimization, Nonlinear Programming, Vol. 4, 1981, pp. 367-394. | MR

[47] E. Sanchez-Palencia, Nonhomogenous Media and Vibration Theory, Springer-Verlag Lecture Notes in Physics, No. 127, 1980. | MR | Zbl

[48] R.T. Rockafellar, First and Second-Order Epi-Differentiability in Nonlinear Programming, Transaction American Mathematical Society, 1988, forthcoming. | MR | Zbl