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Constrained optimization problem

From Encyclopedia of Mathematics
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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.

How to Cite This Entry:
Constrained optimization problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Constrained_optimization_problem&oldid=38540
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article