@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1031, author = {Ivan Ginchev and Armin Hoffmann}, title = {Approximation of set-valued functions by single-valued one}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {22}, year = {2002}, pages = {33-66}, zbl = {1039.90051}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1031} }
Ivan Ginchev; Armin Hoffmann. Approximation of set-valued functions by single-valued one. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 22 (2002) pp. 33-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1031/
[000] [1] J.P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin, Heidelberg, New York, Tokyo 1984. | Zbl 0538.34007
[001] [2] P.K. Belobrov, K voprosu o chebyshevskom sentre mnozhestva, Izvestija vysshich uchebnych zavedenij 38 (1) (1964), 3-9. (in Russian)
[002] [3] B. Bank, J. Guddat, D. Klatte, K. Kummer, K. Tammer, Non-Linear Parametric Optimization, Akademie Verlag Berlin 1982. | Zbl 0502.49002
[003] [4] F.H. Clarke, Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, John Wiley & Sons, New York 1983. | Zbl 0582.49001
[004] [5] V.F. Demjanov and A.M. Rubinov, Constructive Nonsmooth Analysis, Verlag Peter Lang, Frankfurt am Main 1995.
[005] [6] A.L. Garkavi, On the best net and the best cut of a set in a normed space, Izv. Akad. Nauk SSSR, Ser. Mat. 26 (1962), 87-106. (in Russian) | Zbl 0108.10801
[006] [7] A.L. Garkavi, On the Chebyshev center and the convex hull of a set, Usp. Mat. Nauk 19 (6) (1964), 139-145, (120). (in Russian)
[007] [8] A.L. Garkavi, Minimax balayge theorem and an inscribed ball problem, Matematicheskie Zametki 30 (1) (1981), 109-121. (in Russian)
[008] [9] I. Ginchev and A. Hoffmann, On the best approximation of set-valued functions, in: P. Gritzmann, R. Horst, E. Sachs, R. Tichatschke (eds.), Recent Advances in Optimization (Proc. of the 8th French-German Conference on Optimization, Trier, July 21-26, 1996, Lect. Notes Econ. Math. Syst. 452, Springer, Berlin Heidelberg 1997, 61-74. | Zbl 0882.41017
[009] [10] P.M. Gruber, The space of convex bodies, in: P.M. Gruber, J.M. Wills (eds.), Handbook of Convex Geometry, Volume A, North-Holland, Amsterdam 1993, 301-318. | Zbl 0791.52004
[010] [11] R. Hettich and P. Zencke, Numerische Methoden der Approximation und Semi-Infiniten Optimierung, B.G. Teubner, Leipzig 1982. | Zbl 0481.65033
[011] [12] A. Hoffmann, The distance to the intersection of two convex sets expressed by the distances to each of them, Math. Nachr. 157 (1992), 81-98. | Zbl 0773.52002
[012] [13] J.B. Hiriart Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I, Springer Verlag, Berlin 1993.
[013] [14] R.B. Holmes, Geometric Functional Analysis and its Applications, Graduate Texts in Mathematics 24, Springer, New York-Heidelberg-Berlin 1975. | Zbl 0336.46001
[014] [15] R. Horst and H. Tuy, Global Optimization, Deterministic Approaches, Springer, Berlin etc. 1990. | Zbl 0704.90057
[015] [16] P. Kosmol, Optimierung und Approximation, Walter de Gruyter, Berlin 1991.
[016] [17] P.J. Laurent, Approximation et Optimisation, Enseignement des Sciences 13, Hermann, Paris 1972. | Zbl 0238.90058
[017] [18] K. Leichtweiss, Konvexe Mengen, Deutscher Verlag der Wissenschaften, Berlin 1980.
[018] [19] L.E. Rybiński, Continuous Selections and Variational Systems, Monografie 61, Institute of Mathematics, Higher College of Engineering, Zielona Góra, Poland 1992, 100 pp, ISSN 0239-7390. | Zbl 0789.54024
[019] [20] R.T. Rockafellar and R.J.B. Wets, Variational Analysis, Grundlehren der mathematischen Wissenschaften 317, Springer, Berlin 1998.
[020] [21] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Grundlehren der mathematischen Wissenschaften 171, Springer, Berlin 1970.