Transportation flow problems with Radon measure variables
Marcus Wagner
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 20 (2000), p. 93-111 / Harvested from The Polish Digital Mathematics Library
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For a multidimensional control problem (P)K involving controls u∈L∞, we construct a dual problem (D)K in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of (L∞)*. For this purpose, we add to (P)K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:271477 
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Marcus Wagner. Transportation flow problems with Radon measure variables. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 20 (2000) pp. 93-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1007/

[000] [1] H.W. Alt, Lineare Funktionalanalysis, Springer, New York-Berlin 1992.

[001] [2] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston-Basel-Berlin 1990.

[002] [3] C. Carathéodory, Vorlesungen über reelle Funktionen, Chelsea, New York 1968.

[003] [4] N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, Wiley-Interscience, New York 1988. | Zbl 0635.47001

[004] [5] R.V. Gamkrelidze, Principles of Optimal Control Theory, Plenum Press, New York-London 1978. | Zbl 0401.49001

[005] [6] F. Hüseinov, Approximation of Lipschitz functions by infinitely differentiable functions with derivatives in a convex body, Turkish J. of Math. 16 (1992), 250-256. | Zbl 0849.41026

[006] [7] R. Klötzler, On a general conception of duality in optimal control, in: Equadiff IV (Proceedings). Springer, New York-Berlin 1979. (Lecture Notes in Mathematics 703) | Zbl 0404.49022

[007] [8] R. Klötzler, Optimal transportation flows, Journal for Analysis and its Applications 14 (1995), 391-401. | Zbl 0910.49015

[008] [9] R. Klötzler, Strong duality for transportation flow problems, Journal for Analysis and its Applications 17 (1998), 225-228. | Zbl 1032.49039

[009] [10] H. Kraut, Optimale Korridore in Steuerungsproblemen, Dissertation, Karl-Marx-Universität Leipzig 1990. | Zbl 0722.49002

[010] [11] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin-Heidelberg-New York 1966 (Grundlehren 130). | Zbl 0142.38701

[011] [12] S. Pickenhain and M. Wagner, Critical points in relaxed deposit problems, in: A. Ioffe, S. Reich, I. Shafrir, eds., Calculus of variations and optimal control, Technion 98, Vol. II (Research Notes in Mathematics, Vol. 411), Chapman & Hall/CRC Press; Boca Raton, 1999, 217-236. | Zbl 0960.49021

[012] [13] S. Pickenhain and M. Wagner, Pontryagin's principle for state-constrained control problems governed by a first-order PDE system, BTU Cottbus, Preprint-Reihe Mathematik M-03/1999. To appear in: JOTA.

[013] [14] T. Roubicek, Relaxation in Optimization Theory and Variational Calculus, De Gruyter, Berlin-New York 1997. | Zbl 0880.49002

[014] [15] M. Wagner, Erweiterungen eines Satzes von F. Hüseinov über die C∞-Approximation von Lipschitzfunktionen, BTU Cottbus, Preprint-Reihe Mathematik M-11/1999.