@article{AIHPC_1988__5_6_537_0,
author = {Az\'e, Dominique and Attouch, Hedy and Wets, Roger J.-B.},
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},
publisher = {Gauthier-Villars},
volume = {5},
number = {6},
year = {1988},
mrnumber = {978671},
zbl = {0667.49009},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/}
}
TY - JOUR AU - Azé, Dominique AU - Attouch, Hedy AU - Wets, Roger J.-B. TI - Convergence of convex-concave saddle functions : applications to convex programming and mechanics JO - Annales de l'I.H.P. Analyse non linéaire PY - 1988 SP - 537 EP - 572 VL - 5 IS - 6 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/ LA - en ID - AIHPC_1988__5_6_537_0 ER -
%0 Journal Article %A Azé, Dominique %A Attouch, Hedy %A Wets, Roger J.-B. %T Convergence of convex-concave saddle functions : applications to convex programming and mechanics %J Annales de l'I.H.P. Analyse non linéaire %D 1988 %P 537-572 %V 5 %N 6 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/ %G en %F AIHPC_1988__5_6_537_0
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, Tome 5 (1988) no. 6, pp. 537-572. http://archive.numdam.org/item/AIHPC_1988__5_6_537_0/
[1] , Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc., Vol. 123, 1966, pp. 32-45. | MR | Zbl
[2] , Convergence of Convex Sets and Solutions of Variational Inequalities, Advances Math., Vol. 3, 1969, pp. 510-585. | MR | Zbl
[3] , 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] , Variational Convergence for Functions and Operators, Applicable Mathematics Series, Pitman, London, 1984. | MR | Zbl
[5] , On the Continuity of the Young-Fenchel Transform, J. Math. Anal. Appl., Vol. 35, 1971, pp. 518-535. | MR | Zbl
[6] , 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] , Continuity of the Fenchel Transform of Convex Functions, Proceedings of the American Mathematical Society, Vol. 97, 1986, pp. 661-667. | MR | Zbl
[8] , A General Correspondence Between Dual Minimax Problems and Convex Programs, Pacific J. Math., Vol. 25, 1968, pp. 597-611. | MR | Zbl
[9] and , Convex Analysis and Variational Problems, North Holland, Amsterdam, 1978.
[10] and , A Convergence Theory for Saddle Functions, Trans. Amer. Math. Soc., Vol. 280, 1983, pp. 1-44. | MR | Zbl
[11] and , 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] , Alcune caratterizzazioni della Γ-convergenza multipla, Annali Mat. Pura Applicata, Vol. 32, 1982, pp. 69-112.
[13] , 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] , Saddle Topology and Min-Max Theorems, Tech. Report. Univ. Trento., 1984.
[15] , Convergence au sens de Mosco; théorie et applications à l'approximation des solutions d'inéquations, Thèse d'État, Marseille, 1982.
[16] and , 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] , Monotone operators Associated with Saddle Functions and Minimax Problems, in Nonlinear Functional Analysis, American Mathematical Society, Rhode Island, 1970. | MR | Zbl
[18] , Minimax Theorems and Conjugate Saddle Functions, Matematica Scandinavica, Vol. 14, 1964, pp. 151-173. | MR | Zbl
[19] , 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] , Dual Operations on Saddle Functions, Trans. Amer. Math. Soc., Vol. 179, 1973, pp. 363-381. | MR | Zbl
[21] , L'Analyse Non Linéaire et ses Motivations Économiques, Masson, 1984. | MR | Zbl
[22] , Conjugate Duality and Optimization, Regional Conference Series in Applied Mathematics, 16, S.I.A.M., Philadelphia, 1974. | MR | Zbl
[23] , 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] , Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York, 1983. | MR | Zbl
[25] and , Preservation of Convergence of Convex Sets and Functions in Finite Dimensions, Trans. Amer. Math. Soc., Vol. 268, 1981. | MR | Zbl
[26] , Fonctionnelles convexes, séminaire équations aux dérivées partielles, Collège de France, Paris, 1966.
[27] , Une famille de topologies et de convergences sur l'ensemble des fonctionnelles convexes, Thèse d'état, Grenoble, 1970.
[28] , Mathematical Methods of Game and Economic Theory, North Holland, 1979. | MR | Zbl
[29] , On Stability Analysis in Mathematical Programming, Mathematical Programming study, Vol. 21, 1984, pp. 227-242. | MR
[30] , Successive Approximation and Linear Stability Involving Convergent Sequences of Optimization Problems, J. Approximation Theory, Vol. 35, 1982, pp. 311-354. | MR | Zbl
[31] and , Closure and Upper Semicontinuity in Mathematical Programming, Nash and economic equilibria, Tech. Report, Univ. Genova, 1984.
[32] , Stability Results in Convex Programming, Technical Report 85-04, A.V.A.M.A.C., Perpignan, 1985.
[33] , and , Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR | Zbl
[34] , Cours Peccot au collège de France, Paris, 1977.
[35] and , Su un tipo di convergenza variationale, Atti. Accad. Naz. Lincei, Rend. de sc. Mat., (8), Vol. 58, 1975, pp. 842-850. | MR | Zbl
[36] , Periodic Solutions and Homogenization of Non Linear Variational Problems, Ann. Mat. Pura Appl., Vol. 117, 1978, pp. 139-159. | MR | Zbl
[37] and , Boundary value problems in domains with close-grained Boundaries (Russian), Naukova Dumka, Kiev, 1974.
[38] , 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] , Plasticité et homogénéisation, Thèse d'état, Paris-VI, 1982.
[40] , 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] and , Les inéquations en mécanique et en physique, Dunod, 1972. | MR | Zbl
[42] , Optimisation: Méthodes numériques, Masson, 1976. | MR | Zbl
[43] , 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] , 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] , H-Convergence, Rapport du séminaire d'analyse fonctionnelle et numérique, Université d'Alger, 1978.
[46] , 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] and , Approximation and Convergence in Nonlinear Optimization, Nonlinear Programming, Vol. 4, 1981, pp. 367-394. | MR
[47] , Nonhomogenous Media and Vibration Theory, Springer-Verlag Lecture Notes in Physics, No. 127, 1980. | MR | Zbl
[48] , First and Second-Order Epi-Differentiability in Nonlinear Programming, Transaction American Mathematical Society, 1988, forthcoming. | MR | Zbl
