Difference between revisions of "Constrained optimization problem"
From Encyclopedia of Mathematics
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| − | A problem in which a function | + | 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 [[ | + | See also [[Linear programming]]; [[Mathematical programming]]; [[Discrete programming]]; [[Integer programming]]. |
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Latest revision as of 20:16, 3 April 2016
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=15493
Constrained optimization problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Constrained_optimization_problem&oldid=15493
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article