100 40
 8080
 60 60
 U-O



 40
 80
 0 0



 Figure 4.1: Single-peak function

Direct methods seek local optima by moving in a direction related to the local gradient.

This is similar to the method of steepest-descent discussed in Chapter 3. Both methods

are local in scope, that is, the optimum is the best in a neighborhood of the current point.

In terms of the direct search methods the multiple peak function shown in figure 4.2

proves to be a bit of a challenge. In this case it would be difficult to determine which

peak to climb and once an alleged solution is found it is not known whether it is a local or

a global optimum. In addition, search and optimization problems can be multi-modal,

noisy search spaces that can be rife with discontinuities. The calculus-based methods are

practical for certain types of problems.