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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page 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 PDF BibTeX XML Cite \textit{R. Lucchetti} and \textit{F. Patrone}, J. Math. Anal. Appl. 88, 204--215 (1982; Zbl 0487.49013) Full Text: DOI 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 [4] Holmes, R.B, A course on optimization and best approximation, () · Zbl 0234.46016 [5] Kothe, G, Topological vector spaces I∘, (1969), Springer-Verlag Berlin [6] Kuratowsky, C, Topologie, (1948), Wroclaw Warszawa [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 [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) [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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.