Abstract
We study optimal control problems for semilinear elliptic equations
subject to control and state inequality constraints.
Both boundary control and distributed control problems are considered
with boundary conditions of Dirichlet or Neumann type.
By introducing suitable discretization schemes, the control problem
is transcribed into a nonlinear programming problem.
Necessary conditions of optimality are discussed both for the
continuous and the discretized control problem.
It is shown that the recently developed interior point method
LOQO of [35] is capable of solving
these problems even for high discretizations.
Four numerical examples with Dirichlet and Neumann boundary conditions
are provided that illustrate the performance of the algorithm for different types of controls including bang-bang
controls.
Keywords
Elliptic control problems, boundary and distributed control,
control and state constraints, discretization techniques,
interior point optimization methods