  We consider a linear symmetric and elliptic PDE and a linear goal functional.
We design and analyze a goal-oriented adaptive finite element method, which
steers the adaptive mesh-refinement as well as the approximate solution of the
arising linear systems by means of a contractive iterative solver like the
optimally preconditioned conjugate gradient method or geometric multigrid. We
prove linear convergence of the proposed adaptive algorithm with optimal
algebraic rates. Unlike prior work, we do not only consider rates with respect
to the number of degrees of freedom but even prove optimal complexity, i.e.,
optimal convergence rates with respect to the total computational cost.
