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Continuous dependence on data in abstract control problems. (English) Zbl 0521.49021


MSC:

49K40 Sensitivity, stability, well-posedness
49K27 Optimality conditions for problems in abstract spaces
93C25 Control/observation systems in abstract spaces
46C99 Inner product spaces and their generalizations, Hilbert spaces
49J45 Methods involving semicontinuity and convergence; relaxation
49N15 Duality theory (optimization)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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References:

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[2] Lucchetti, R., andMignanego, F.,Continuous Dependence on the Data in Abstract Control Problems, Journal of Optimization Theory and Applications, Vol. 34, pp. 423–444, 1981. · Zbl 0431.49028 · doi:10.1007/BF00934681
[3] Bennati, M. L.,On the Convergence of the Dual Variables in Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 34, pp. 263–278, 1981. · Zbl 0431.49026 · doi:10.1007/BF00935476
[4] Zolezzi, T.,Variational Stability and Well-Posedness in the Optimal Control of Ordinary Differential Equations, Paper Presented at the Mathematical Theory of Optimal Control Seminar, Stefan Banach International Center, Warsaw, Poland, 1980.
[5] Sonntag, Y.,Interprétation Géométrique de la Convergence d’une Suite de Convexes, Exposé Multigraphié du Séminaire de Mathématiques Appliquées, Université de Provence, 1976.
[6] Sonntag, Y.,Convergence au Sense de U. Mosco, Université de Provence, Thèse d’État, 1982.
[7] Barbu, V., andPrecupanu, T.,Convexity and Optimization in Banach Spaces, Sijthoff and Noordhoff, Alphen aan de Rijn, Holland, 1978. · Zbl 0379.49010
[8] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[9] ZĂlinescu, C.,On Uniformly Convex Functions, Journal of Mathematical Analysis and Applications, Vol. 95, pp. 344–374, 1983. · Zbl 0519.49010 · doi:10.1016/0022-247X(83)90112-9
[10] ZĂlinescu, C., Duality for Vectorial Nonconvex Optimization by Convexification and Applications, Analele Stiintifice ale Universit306-3tii ”Al. I. Cuza” din Iasi, s. I-a. Matematic306-4, Vol. 29, pp. 15–34, 1983.
[11] Diestel, J.,Geometry of Banach spaces–Selected Topics, Springer-Verlag, Berlin, Germany, 1975. · Zbl 0307.46009
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