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Lucchetti, Roberto; Patrone, Fioravante

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

J. Math. Anal. Appl. 88, 204-215 (1982).
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Cited in 30 Documents

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)

Keywords:

Tychonov well-posedness; Hadamard well-posedness; well-posedness for minimum problems; minimizing sequence; Hausdorff convergence; Mosco’s convergence
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\textit{R. Lucchetti} and \textit{F. Patrone}, J. Math. Anal. Appl. 88, 204--215 (1982; Zbl 0487.49013)
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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 Paris
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[7] Lucchetti, R; Patrone, F, Metodo ε e convergenza di mosco, (), 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
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[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)
[13] {\scT. Zolezzi}, A characterization of well-posed optimal control systems, SIAM J. Control Optim., in press. · Zbl 0469.49021
[14] Zolezzi, T, Characterization of some variational perturbations of the abstract linearquadratic problem, SIAM J. control optim., 18, 106, (1978) · Zbl 0391.49019
[15] {\scT. Zolezzi}, in preparation.
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