“A lens is about as nonlinear as anything in physics.”
What is usually referred to as automatic lens design is, of course, nothing of the sort. The computer programs so described are actually optimization programs that drive an optical design to a local optimum, as defined by a merit function (which is not a true merit function, but actually a defect or error function). In spite of the preceding disclaimers, we will use these commonly accepted terms in the discussions that follow.
The lens design program typically operates this way: Each variable parameter is changed (one at a time) by a small increment whose size is chosen as a compromise between ...