# Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas; Fredi Tröltzsch

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 3, page 581-600
- ISSN: 1292-8119

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topCasas, Eduardo, and Tröltzsch, Fredi. "Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 581-600. <http://eudml.org/doc/250737>.

@article{Casas2010,

abstract = { Optimal control problems for semilinear elliptic equations
with control constraints and pointwise state constraints are
studied. Several theoretical results are derived, which are
necessary to carry out a numerical analysis for this class of
control problems. In particular, sufficient second-order optimality
conditions, some new regularity results on optimal controls and a
sufficient condition for the uniqueness of the Lagrange multiplier
associated with the state constraints are presented.
},

author = {Casas, Eduardo, Tröltzsch, Fredi},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; pointwise state constraints; first and second order optimality conditions; Lagrange multipliers; Borel measures; optimal control},

language = {eng},

month = {7},

number = {3},

pages = {581-600},

publisher = {EDP Sciences},

title = {Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems},

url = {http://eudml.org/doc/250737},

volume = {16},

year = {2010},

}

TY - JOUR

AU - Casas, Eduardo

AU - Tröltzsch, Fredi

TI - Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/7//

PB - EDP Sciences

VL - 16

IS - 3

SP - 581

EP - 600

AB - Optimal control problems for semilinear elliptic equations
with control constraints and pointwise state constraints are
studied. Several theoretical results are derived, which are
necessary to carry out a numerical analysis for this class of
control problems. In particular, sufficient second-order optimality
conditions, some new regularity results on optimal controls and a
sufficient condition for the uniqueness of the Lagrange multiplier
associated with the state constraints are presented.

LA - eng

KW - Optimal control; pointwise state constraints; first and second order optimality conditions; Lagrange multipliers; Borel measures; optimal control

UR - http://eudml.org/doc/250737

ER -

## References

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## Citations in EuDML Documents

top- Arnd Rösch, Simeon Steinig, error estimates for a state-constrained elliptic optimal control problem
- Arnd Rösch, Simeon Steinig, A priori error estimates for a state-constrained elliptic optimal control problem
- Arnd Rösch, Simeon Steinig, error estimates for a state-constrained elliptic optimal control problem
- Eduardo Casas, Mariano Mateos, Boris Vexler, New regularity results and improved error estimates for optimal control problems with state constraints

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