Global optimization involves finding the absolute maximum or minimum value of a function (the objective function) of several variables, possibly subject to restrictions (defined by a set of bounds or constraint functions) on the values of the variables. Such problems can be much harder to solve than local optimization problems (which are discussed in E04 class) because it is difficult to determine whether a potential optimum found is global, and because of the nonlocal methods required to avoid becoming trapped near local optima. Most optimization methods in the NAG Library are concerned with function minimization only, since the problem of maximizing a given objective function $F$ is equivalent to minimizing $-F$. In e05jb, (E05SAF not in this release) and (E05SBF not in this release), you may specify whether you are solving a minimization or maximization problem; in the latter case, the required transformation of the objective function will be carried out automatically. In what follows we refer exclusively to minimization problems.

This introduction is a brief guide to the subject of global optimization, designed for the casual user. For further details you may find it beneficial to consult a more detailed text, such as Neumaier (2004). Furthermore, much of the material in the E04 class is relevant in this context also. In particular, it is strongly recommended that you read [] in the E04 class Chapter Introduction.