| OCR Text |
Show 60 known as optimization. Since the functions we are optimizing are not necessarily linear we must utilize the techniques of non-linear optimizaton. Finally, we are interested in only those local maxima within the patch parameter limits from 0 to 1. This problem is called constrained non-linear optimization. There have been whole books written on this specific topic but most of the techniques described therein are not applicable to this problem. The typical non-linear optimization problem deals with functions of a great many variables for which the derivatives are not known. Using these algorithms would be overly complicated and not take advantage of the knowledge we have about the derivatives. Univariate Optimization We begin, again, by first considering the unconstrained univariate case. That is, given the function f(u), and an initial guess uO, find the neaest local maximum. There are two conditions which must be satisfied for a local maximum to occur. They are 1) f I (u) 0 2) f"(u) < 0 It is still possible to have a local maximum if f"=O but higher order derivatives need to be examined. |
