Numerical aspects of a level set based algorithm for state constrained optimal control problems

Abstract

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 an useful extension of this gradient (naturally defined only on the interface) to the whole computational domain are discussed.