## The Euler approximation in state constrained optimal control

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- by A. L. Dontchev and William W. Hager;
- Math. Comp.
**70**(2001), 173-203 - DOI: https://doi.org/10.1090/S0025-5718-00-01184-4
- Published electronically: April 13, 2000
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## Abstract:

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition and the Lagrangian satisfies a coercivity condition, then locally there exists a solution to the Euler discretization, and the error is bounded by a constant times the mesh size. The proof couples recent stability results for state constrained control problems with results established here on discrete-time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invoked.## References

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## Bibliographic Information

**A. L. Dontchev**- Affiliation: Mathematical Reviews, Ann Arbor, Michigan 48107
- Email: ald@ams.org
**William W. Hager**- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: hager@math.ufl.edu
- Received by editor(s): October 15, 1998
- Received by editor(s) in revised form: February 16, 1999
- Published electronically: April 13, 2000
- Additional Notes: This research was supported by the National Science Foundation.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp.
**70**(2001), 173-203 - MSC (2000): Primary 49M25, 65L10, 65L70, 65K10
- DOI: https://doi.org/10.1090/S0025-5718-00-01184-4
- MathSciNet review: 1681116