Automatic computing methods are being increasingly applied to optical design, and the development of programs for this purpose forms an interesting chapter in optical history. Mathematically, the problem consists of solving sets of simultaneous nonlinear equations in a space of thirty or more variables limited by prescribed boundaries. Although these boundary conditions do not basically alter the mathematics, they greatly complicate the resulting program, and a specific example reveals how intricate such programs can become. The full impact of automatic methods has not yet been felt, but one result should be to shift the attention of the lens designer from the detailed correction of aberrations to the problem of securing a proper compromise between the system requirements and the conditions for sharp imagery so that better balanced optical instruments may result.
Donald P. Feder, "Automatic Optical Design," Appl. Opt. 2, 1209-1226 (1963)