  In this paper, we study an optimal control problem for a macroscopic
mechanical tumour model based on the phase field approach. The model couples a
Cahn--Hilliard type equation to a system of linear elasticity and a
reaction-diffusion equation for a nutrient concentration. By taking advantage
of previous analytical well-posedness results established by the authors, we
seek optimal controls in the form of a boundary nutrient supply, as well as
concentrations of cytotoxic and antiangiogenic drugs that minimise a cost
functional involving mechanical stresses. Special attention is given to
sparsity effects, where with the inclusion of convex non-differentiable
regularisation terms to the cost functional, we can infer from the first-order
optimality conditions that the optimal drug concentrations can vanish on
certain time intervals.
