  We consider optimal control problems that have binary-valued control input
functions and a perimeter regularization. We develop and analyze a trust-region
algorithm that solves a sequence of subproblems in which the regularization
term and the binarity constraint are relaxed by a non-convex energy functional.
We show how the parameter that controls the distinctiveness of the resulting
phase field can be coupled to the trust-region radius updates and be driven to
zero over the course of the iterations in order to obtain convergence to
stationary points of the limit problem under suitable regularity assumptions.
Finally, we highlight and discuss the assumptions and restrictions of our
approach and provide the first computational results for a motivating
application in the field of control of acoustic waves in dissipative media.
