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We consider optimal control problems that have binary-valued control inputfunctions and a perimeter regularization. We develop and analyze a trust-regionalgorithm that solves a sequence of subproblems in which the regularizationterm and the binarity constraint are relaxed by a non-convex energy functional.We show how the parameter that controls the distinctiveness of the resultingphase field can be coupled to the trust-region radius updates and be driven tozero over the course of the iterations in order to obtain convergence tostationary points of the limit problem under suitable regularity assumptions.Finally, we highlight and discuss the assumptions and restrictions of ourapproach and provide the first computational results for a motivatingapplication in the field of control of acoustic waves in dissipative media.

Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control