Constrained optimization problem

A problem in which a function $f(x)$ is to be optimized (i.e., minimized or maximized) subject to the requirement that the possible solutions lie in a so-called feasible set $X$. The set $X$ is usually determined by constraints. Frequently occurring constraints are: $g(x) \le b$, where $g$ is a function; $x_j \in \mathbf{Z}$ (where $x_j$ is the $j$-th component of $x$), an integrality constraint; or $x_j \in \{0,1\}$, a binary constraint.

See also Linear programming; Mathematical programming; Discrete programming; Integer programming.