Title: A convex penalty for switching control of partial differential equations,
Abstract: A convex penalty for promoting switching controls for partial differential
equations is introduced; such controls consist of an arbitrary number of
components of which at most one should be simultaneously active. Using a
Moreau-Yosida approximation, a family of approximating problems is obtained
that is amenable to solution by a semismooth Newton method. The efficiency of
this approach and the structure of the obtained controls are demonstrated by
numerical examples.