  We consider a linear elliptic PDE and a quadratic goal functional. The
goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a
dual problem, where the goal functional is always linearized around the
discrete primal solution at hand. We show that the marking strategy proposed in
[Feischl et al, SIAM J. Numer. Anal., 54 (2016)] for a linear goal functional
is also optimal for quadratic goal functionals, i.e., GOAFEM leads to linear
convergence with optimal convergence rates.
