# Transportation flow problems with Radon measure variables

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

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

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topMarcus 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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- [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] 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.
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- [15] M. Wagner, Erweiterungen eines Satzes von F. Hüseinov über die ${C}^{\infty}$-Approximation von Lipschitzfunktionen, BTU Cottbus, Preprint-Reihe Mathematik M-11/1999.

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