Minimization of computational work for elliptic and related problems, including boundary value problems for strongly elliptic systems and corresponding eigenvalue problems, is one of the most important and difficult problems of computational mathematics. Since the problem is closely connected with asymptotically optimal approximations involving a minimal number N = N(e) of degrees of freedom to get a desired accuracy € > 0 of the approximation, it has many common features with classical optimization problems of approximation theory and numerical integration.