  We consider a linear symmetric and elliptic PDE and a linear goal functional.
We design a goal-oriented adaptive finite element method (GOAFEM), 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 (PCG). We prove linear convergence of
the proposed adaptive algorithm with optimal algebraic rates with respect to
the number of degrees of freedom as well as the computational cost.
