On primal-dual stability in convex optimization

Journal of Convex Analysis

Volumn 3, Issue 2, 1996, Pages 309-327

  Azé, Dominique ^a   Rahmouni, Abdelouahed ^a  

^a UNIVERSITÉ DE PERPIGNAN   (France)

Author keywords

[No Author keywords available]

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EID: 21744442526     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. H. Attouch: Variational convergence for functions and operators, Applicable Mathematics Series, Pitman, Boston, London, 1984.
2. H. Attouch, D. Azé and R.J.-B. Wets: Convergence of convex- concave saddle functions: applications to convex programming and mechanics, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5 (1988) 537-572.
3. H. Attouch, G. Beer: On the convergence of subdifferential of convex functions, Arch. Math. 60 (1993) 389-400.
4. D. Azé: Duality for the sum of convex functions in general normed spaces, Arch. Math. 6 (1994) 554-561.
5. D. Azé, J.-P. Penot: Operations on convergent families of sets and functions, Optimization 21 (1990) 521-534.
6. D. Azé, J.-P. Penot: Qualitative results about the convergence of convex sets and convex functions, A. Ioffe, M. Marcus and S. Reich eds, Pitman Research Notes in Mathematics Series (1992) 1-24.
7. D. Azé, J.-P. Penot: The JoIy topology and the Mosco-Beer topology revisited, Bull. Austral. Math. Soc. 48 (1993) 353-364.
8. D. Azé: On optimality conditions for state-constrained optimal control problems governed by partial differential equations, submitted, 1994.
9. K. Back: Continuity of the Fenchel transform of convex functions, Proc. Am. Math. Soc. 97 (1986) 661-667.
10. K. Back: Convergence of Lagrange multipliers and dual variables for convex optimization problems, Math. Op. Res. 13 (1990) 74-79.
11. G. Beer: The slice topology, a viable alternative to Mosco convergence in nonreflexive spaces, Nonlinear Analysis, Theory Methods Appl. 19 (1992) 271-290.
12. G. Beer: Topologies on closed and closed convex sets, Mathematics and its applications, 268, Kluwer, London, Dordrecht, Boston, 1994.
13. R.C. Bergström: Optimization, Convergence and Duality, Ph. D. Thesis, University of Illinois at Urbana-Champaign, 1980.
14. I. Ekeland, R. Temam: Analyse convexe et problèmes variationnels, Dunod, Paris, 1978.
15. E.G. GoPštein Theory of convex programming, Translations of mathematical monograph, Volume 36, American Mathematical Society, Providence, 1972.
16. J.-L. Joly: Une famille de topologies et de convergences sur l'ensemble des fonctionnelles convexes, Thèse ď état, Université de Grenoble, 1970.
17. J.-L. JoIy: Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarité est bicontinue, J. Math. Pures Appl., IX. Sér., 52 (1973) 421-441.
18. J. Lahrache: Topologie sur l'ensemble des convexes fermés d'un espace vectoriel normé, stabilité et analyse unilatérale, Thèse, Université de Montpellier, 1992.
19. J. Lahrache: Stabilité et convergence dans les espaces non réflexifs, Sémin. Anal. Convexe, Univ. Sci. Tech. Languedoc, exposé n° 10, 1991.
20. P.-J. Laurent: Approximation et Optimisation, Hermann, Paris, 1972.
21. R. Lucchetti, F. Patrone: Closure and upper semicontinuity results in mathematical programming, Nash and economic equilibria, Optimization 17 (1986) 619-628.
22. J.-L. Lions and E. Magenes: Problèmes aux limites non homogènes et applications, Dunod, Gauthier-Villars, Paris, 1968.
23. L. Mc Linden, R.C. Bergström: Preservation of convergence of convex sets and functions in finite dimensions, Trans. Am. Math. Soc. 268 (1981) 127-142.
24. J.-J. Moreau, Fonctionnelles convexes: Lecture Notes Collège de France, Paris, 1966.
25. U. Mosco: Convergence of convex sets and of solutions of variational inequalities, Adv. Math. 3 (1969) 510-585.
26. U. Mosco: On the continuity of the Young-Fenchel transform, J. Math. Anal. Appl. 45 (1974) 533-555.
27. H. Riahi: Quelques résultats de stabilité en analyse épigraphique: approche topologique et quantitative, Thèse, University of Montpellier, France, 1989.
28. S.M.Robinson: Regularity and stability for convex multivalued functions, Math. Oper. Res. 1 (1976) 130-143.
29. R.T. Rockafellar: Conjugate duality and optimization, SIAM publication 16, Philadelphia, 1974.
30. R. Schultz: Estimates for Kuhn-Tucker points of perturbed convex programs, Optimization 19 (1988) 29-43.
31. Y. Sonntag, C. Zalinescu: Set convergence. An attempt of classification, International Conference on Differential Equations and Control Theory, Iaşi, Romania, 1990.
32. Y. Sonntag, C. Zalinescu: Set convergence. An attempt of classification, Trans. Am. Math. Soc. 340 (1993) 199-226.
33. Y. Sonntag, C. Zalinescu: Set convergence: a survey and a classification, Set Valued Analysis 2 (1994) 339-356.
34. R. Vinter: Convex duality and nonlinear optimal control, SIAM J. Control Opt. 31 (1993) 518-538.