Nonlinear problems

All the least squares problems in earlier chapters are merely the first step in a wider class of problems--nonlinear problems. Nonlinear problems typically arise when the unknowns come in two flavors. The slogan ``don't add apples to oranges'' applies in reverse, if you have apples and oranges, it is unlikely they will be combined by simple addition--a more complicated nonlinear relationship likely relates the unknowns. Linear relationships apply when we pretend that apples are constant while we solve for the oranges, and vice versa. The nonlinear relationships we will study here are little more than a systematic way of letting everything vary at once.