ABSTRACT
The single-variable optimization problem is of a central importance to optimization and practice. Not only because it is a type of problem that engineers encounter in practice, but because more general problem with n variables can often be solved by a sequence of one-variable problems. In this chapter we will introduce some basic numerical methods for locating the minimum of a function in one variable. We will only consider minimization problems with the understanding that maximizing f(x) is the same as minimizing −f(x). To introduce the idea consider the following example:
L depends on the angle α. That is,
L(α) = L1 + L2 = 3
sinα +
cosα .
