@article{1059.65057,
author="Hinterm\"uller, Michael and Ring, Wolfgang",
title="{A level set approach for the solution of a state-constrained optimal
    control problem.}",
language="English",
journal="Numer. Math. ",
volume="98",
number="1",
pages="135-166",
year="2004",
doi={10.1007/s00211-004-0531-z},
abstract="{The authors consider state constrained optimal control problems for
    linear elliptic partial differential equations of the type $$\gather\min
    J(y,u)= {1\over 2}\Vert y- y_d\Vert^2_{L^2(\Omega)}+ {\alpha\over 2} \Vert
    u\Vert^2_{L^2(\Omega)}\\ \text{subject to }\Delta y+ u= 0\quad\text{on
    }\Omega\quad\text{and }y\le\psi\quad\text{on }\Omega.\endgather$$ Analyzing
    the corresponding first-order optimality conditions an algorithm is given
    which is based on the level set methodology. Numerical tests are given.}",
reviewer="{Hans Benker (Merseburg)}",
keywords="{state constrained optimal control; linear elliptic partial
    differential equations; algorithm; level set method; numerical examples}",
classmath="{*65K10 (Optimization techniques (numerical methods))
49J20 (Optimal control problems with PDE (existence))
49Q10 (Optimization of the shape other than minimal surfaces)
49M25 (Finite difference methods)
}",
}