A projection apparatus for microlithography comprising - an objective for imaging an object field, - at least one or a plurality of manipulators for manipulating at least one or a plurality of optical elements of the objective, - a control unit for controlling the at least one or the plurality of manipulators, - a determining device for determining at least one image aberration, characterized in that the projection apparatus comprises - a memory containing upper bounds for one or a plurality of specifications of the objective, including upper bounds for the at least one image aberration and the movements of the at least one or the plurality of manipulators, and that the control unit - contains a first device configured to determine a movement distance of the at least one or the plurality of manipulators by solving an inverse problem according to the manipulator actuating distances, - contains a second device configured to numerically stabilize the inverse problem by a numerical stabilization, the numerical stabilization is a Tikhonov stabilization with weight matrix G or weight γ, in particular an L-curve method, - contains a third device configured to convert the inverse problem into a minimization problem, - contains a fourth device configured to convert the upper bounds into boundary conditions for the minimization problem, - contains a fifth device configured to solve the minimization problem, in particular by means of linear programming, in particular the Simplex method, or quadratic programming or a quasi-Newton method or a cg method or an interior point method or an active sets method or simulated annealing or sequential quadratic programming or a genetic algorithm or a ruin and recreate method or by means of toggling two or a finite set of the above methods. - an objective for imaging an object field, - at least one or a plurality of manipulators for manipulating at least one or a plurality of optical elements of the objective, - a control unit for controlling the at least one or the plurality of manipulators, - a determining device for determining at least one image aberration, - a memory containing upper bounds for one or a plurality of specifications of the objective, including upper bounds for the at least one image aberration and the movements of the at least one or the plurality of manipulators, - contains a first device configured to determine a movement distance of the at least one or the plurality of manipulators by solving an inverse problem according to the manipulator actuating distances, - contains a second device configured to numerically stabilize the inverse problem by a numerical stabilization, the numerical stabilization is a Tikhonov stabilization with weight matrix G or weight γ, in particular an L-curve method, - contains a third device configured to convert the inverse problem into a minimization problem, - contains a fourth device configured to convert the upper bounds into boundary conditions for the minimization problem, - contains a fifth device configured to solve the minimization problem, in particular by means of linear programming, in particular the Simplex method, or quadratic programming or a quasi-Newton method or a cg method or an interior point method or an active sets method or simulated annealing or sequential quadratic programming or a genetic algorithm or a ruin and recreate method or by means of toggling two or a finite set of the above methods.