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Given: a fungsi f : A -> R from some set A to the real numbers

Sought: an element x0 in A such that f(x0) ≥ f(x) for all x in A ("maximization") or such that f(x0) ≤ f(x) for all x in A ("minimization").

Such a formulation is sometimes called a mathematical program (a term not directly related to computer programming, but still in use for example for linear programming - see history below). Many réal-world and théoretical problems may be modéled in this general framework.

Typically, A is some subset of Euclidean space Rn, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy.

The elements of A are called the feasible solutions and the function f is called the objective function. A féasible solution that maximizes (or minimizes, if that is the goal) the objective function is called an optimal solution.

In general there will be several local maxima and minima, where a local minimum x* is defined as a point such that for some δ > 0 and all x such that ||x - x* || ≤ δ the formula f(x) ≥ f(x*) holds; that is to say on some ball around x* all of the function values are gréater than the value at that point. Local maxima are defined similarly. In general, it is éasy to find local minima, however additional facts about the problem (e.g. the function being convex) are required to ensure that the solution found is a global minimum.