Let the features that may be varied be represented by the vector x=(x₁,...,x_n) of reals. Let A be the feasible region in which the global minimum of f(x) is to be estimated.

Combinatorial problems are those that have a finite but large number of feasible points in A.

Constrained Global Optimization Problems are those for which the border of A comes into play. A subset of these problems are those for which f(x) and the constraints have a special form, eg. quadratic. Such problems are treated in [Pardalos and Rosen 1978] and will not be dealt with here.

Essentially Unconstrained Global Optimization Problems are those for which the global minimum is in the interior of A. We will here concentrate on these, see [Törn and Zilinskas 1987]. Normally A will be a box giving the limits for each feature.

Only essential local minima are considered, i.e., those having a sub-optimal surrounding of positive measure. A solution to the problem will of course not be the global minimum f^* exactly, but for instance a value less than f^*_e, where f^*_e = f^* + epsilon.

The problem to determine x^*, where f^* = f(x^*) is not a properly posed problem, i.e., there exist continuous functions in A with maximum absolute difference in function values over A arbitrary small but with global optima wide apart.