  In this paper we study the mixed virtual element approximation to an elliptic
optimal control problem with boundary observations. The objective functional of
this type of optimal control problem contains the outward normal derivatives of
the state variable on the boundary, which reduces the regularity of solutions
to the optimal control problems. We construct the mixed virtual element
discrete scheme and derive a priori error estimate for the optimal control
problem based on the variational discretization for the control variable.
Numerical experiments are carried out on different meshes to support our
theoretical findings.
