A projection exposure apparatus for microlithography comprising: - a projection lens for imaging mask structures, - at least one manipulator (M1-M4), which is configured to change an optical effect of at least one optical element (E1-E4) of the projection lens by manipulating a property of the optical element along a travel, and - a travel establishing device for generating a travel command for the at least one manipulator, wherein: the travel establishing device is configured firstly to generate a first travel command from a first state characterization of the projection lens by executing an optimization algorithm with at least one work variable, the optimization algorithm is configured to change a value of the work variable in the course of the optimization and to save the value of the work variable that is present at the end of the optimization as a transfer value, and the travel establishing device is furthermore configured to generate a further travel command from a further state characterization of the projection lens, said further state characterization being updated relative to the first state characterization, by repeated execution of the optimization algorithm and in the process to use the saved transfer value as a start value of the at least one work variable. - a projection lens for imaging mask structures, - at least one manipulator (M1-M4), which is configured to change an optical effect of at least one optical element (E1-E4) of the projection lens by manipulating a property of the optical element along a travel, and - a travel establishing device for generating a travel command for the at least one manipulator, wherein: the travel establishing device is configured firstly to generate a first travel command from a first state characterization of the projection lens by executing an optimization algorithm with at least one work variable, the optimization algorithm is configured to change a value of the work variable in the course of the optimization and to save the value of the work variable that is present at the end of the optimization as a transfer value, and the travel establishing device is furthermore configured to generate a further travel command from a further state characterization of the projection lens, said further state characterization being updated relative to the first state characterization, by repeated execution of the optimization algorithm and in the process to use the saved transfer value as a start value of the at least one work variable. the travel establishing device is configured firstly to generate a first travel command from a first state characterization of the projection lens by executing an optimization algorithm with at least one work variable, the optimization algorithm is configured to change a value of the work variable in the course of the optimization and to save the value of the work variable that is present at the end of the optimization as a transfer value, and the travel establishing device is furthermore configured to generate a further travel command from a further state characterization of the projection lens, said further state characterization being updated relative to the first state characterization, by repeated execution of the optimization algorithm and in the process to use the saved transfer value as a start value of the at least one work variable.