# Category:Path-constrained arcs

Whenever a path constraint is active, i.e., it holds , and no continuous control can be determined to compensate for the changes in , naturally needs to do so by taking values in the interior of its feasible domain. An illustrating example has been given in [Sager2009]**Author: ** *Sager, S.; Reinelt, G.; Bock, H.G.***Journal: ** *Mathematical Programming***Number: ** *1***Pages: ** *109--149***Title: ** *Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems***Url: ** *http://mathopt.de/PUBLICATIONS/Sager2009.pdf***Volume: ** *118***Year: ** *2009*

, where velocity limitations for the energy-optimal operation of New York subway trains are taken into account. The optimal integer solution does only exist in the limit case of infinite switching (Zeno behavior), or when a tolerance is given.

## References

[Sager2009] | Sager, S.; Reinelt, G.; Bock, H.G. (2009): Direct Methods With Maximal Lower Bound for Mixed-Integer Optimal Control Problems. Mathematical Programming, 118, 109--149 |

## Pages in category "Path-constrained arcs"

The following 9 pages are in this category, out of 9 total.