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Hadamard and Tyhonov well-posedness of a certain class of convex functions. (English) Zbl 0487.49013


MSC:

49K40 Sensitivity, stability, well-posedness
49K27 Optimality conditions for problems in abstract spaces
90C55 Methods of successive quadratic programming type
90C25 Convex programming
90C48 Programming in abstract spaces
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
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References:

[1] Asplund, E.; Rockafellar, R. T., Gradients of convex functions, Trans. Amer. Math. Soc., 139, 443 (1969) · Zbl 0181.41901
[2] Berdisev, V. I., Stability of a minimization problem under perturbation of the set of admissible elements, Math. USSR-Sb., 32, 401 (1977) · Zbl 0396.90077
[3] Ekeland, I.; Teman, R., Analyse convexe et problèmes variationels (1974), Dunod: Dunod Paris · Zbl 0281.49001
[4] Holmes, R. B., A Course on Optimization and Best Approximation, (Lecture Notes in Mathematics No 257 (1972), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0234.46016
[5] Kothe, G., Topological Vector Spaces I∘ (1969), Springer-Verlag: Springer-Verlag Berlin · Zbl 0179.17001
[6] Kuratowsky, C., Topologie (1948), Wroclaw: Wroclaw Warszawa
[7] Lucchetti, R.; Patrone, F., Metodo ε e convergenza di Mosco, (Rend. Sem. Mat. Univ. Padova, 57 (1977)), 1 · Zbl 0403.49032
[8] Mosco, U., Convergence of convex sets and of solutions of variational inequalities, Adv. Math., 3, 510 (1969) · Zbl 0192.49101
[9] Polijak, B. T., Existence theorems with restrictions, Soviet Math. Dokl., 72 (1966)
[10] Rockafellar, R. T., Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc., 123, 46 (1966) · Zbl 0145.15802
[11] Sonntag, Y., Interpretation geometrique de la convergence d’une suite de convexes, C. R. Acad. Sci. Paris Ser. A, 282, 1099 (1976) · Zbl 0328.41026
[12] Tyhonov, A. N., On the stability of the functional optimization problem, Soviet Math. Dokl., 6, 28 (1966) · Zbl 0212.23803
[14] Zolezzi, T., Characterization of some variational perturbations of the abstract linearquadratic problem, SIAM J. Control Optim., 18, 106 (1978) · Zbl 0391.49019
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