Transportation flow problems with Radon measure variables

Marcus Wagner

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)

  • Volume: 20, Issue: 1, page 93-111
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Marcus Wagner. "Transportation flow problems with Radon measure variables." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.1 (2000): 93-111. <http://eudml.org/doc/271477>.

@article{MarcusWagner2000,
abstract = {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.},
author = {Marcus Wagner},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {multidimensional control problems; strong duality; saddle-point conditions; Baire classification; multidimensional control problem},
language = {eng},
number = {1},
pages = {93-111},
title = {Transportation flow problems with Radon measure variables},
url = {http://eudml.org/doc/271477},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Marcus Wagner
TI - Transportation flow problems with Radon measure variables
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2000
VL - 20
IS - 1
SP - 93
EP - 111
AB - 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.
LA - eng
KW - multidimensional control problems; strong duality; saddle-point conditions; Baire classification; multidimensional control problem
UR - http://eudml.org/doc/271477
ER -

References

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  7. [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) Zbl0404.49022
  8. [8] R. Klötzler, Optimal transportation flows, Journal for Analysis and its Applications 14 (1995), 391-401. Zbl0910.49015
  9. [9] R. Klötzler, Strong duality for transportation flow problems, Journal for Analysis and its Applications 17 (1998), 225-228. Zbl1032.49039
  10. [10] H. Kraut, Optimale Korridore in Steuerungsproblemen, Dissertation, Karl-Marx-Universität Leipzig 1990. Zbl0722.49002
  11. [11] C.B. Morrey, Multiple Integrals in the Calculus of Variations, Springer, Berlin-Heidelberg-New York 1966 (Grundlehren 130). Zbl0142.38701
  12. [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. Zbl0960.49021
  13. [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. 
  14. [14] T. Roubicek, Relaxation in Optimization Theory and Variational Calculus, De Gruyter, Berlin-New York 1997. Zbl0880.49002
  15. [15] M. Wagner, Erweiterungen eines Satzes von F. Hüseinov über die C ∞ -Approximation von Lipschitzfunktionen, BTU Cottbus, Preprint-Reihe Mathematik M-11/1999. 

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