An optimization problem involves minimizing a function (called the objective function) of several variables, possibly subject to restrictions on the values of the variables defined by a set of constraint functions. Most methods in the Library are concerned with function minimization only, since the problem of maximizing a given objective function F(x) is equivalent to minimizing $-F\left(x\right)$. Some methods allow you to specify whether you are solving a minimization or maximization problem, carrying out the required transformation of the objective function in the latter case.

In general methods in this chapter find a local minimum of a function $f$, that is a point $x^{*}$ s.t. for all $x$ near $x^{*}f\left(x\right)\ge f\left(x^{*}\right)$.

The E05 class contains methods to find the global minimum of a function $f$. At a global minimum $x^{*}f\left(x\right)\ge f\left(x^{*}\right)$ for all $x$.

The (H not in this release) contains methods typically regarded as belonging to the field of operations research.

This introduction is only a brief guide to the subject of optimization designed for the casual user. Anyone with a difficult or protracted problem to solve will find it beneficial to consult a more detailed text, such as Gill et al. (1981) or Fletcher (1987).