@article{1047.49028,
author="Hinterm\"uller, Michael and Ring, Wolfgang",
title="{Numerical aspects of a level set based algorithm for state constrained
    optimal control problems.}",
language="English",
journal="Comput. Assist. Mech. Eng. Sci. ",
volume="10",
number="2",
pages="149-161",
year="2003",
abstract="{Summary: Numerical aspects of a level set based algorithm for state
    constrained linear-quadratic optimal control problems for elliptic partial
    differential equations are discussed. The speed function needed in the level
    set equation is derived from shape sensitivity analysis. The discretization
    operates on a fixed grid and additional boundary points representing the
    discrete interface between the coincidence set and the set where the bound
    to the state is not active. The discretization of the hyperbolic level set
    equation, the shape gradient of an appropriate penalty functional and a
    useful extension of this gradient (naturally defined only on the interface)
    to the whole computational domain are discussed.}",
keywords="{level set; constrained linear-quadratic optimal control; shape
    sensitivity; discretization; penalty functional}",
classmath="{*49M25 (Finite difference methods)
49N10 (Linear-quadratic optimal control problems)
49Q10 (Optimization of the shape other than minimal surfaces)
49M30 (Methods of successive approximation, not based on necessary cond.)
65K10 (Optimization techniques (numerical methods))
}",
}