@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))
}",
}