View source for Constrained optimization problem

A problem in which a function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103601.png" /> is to be optimized (i.e., minimized or maximized) subject to the requirement that the possible solutions lie in a so-called feasible set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103602.png" />. The set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103603.png" /> is usually determined by constraints. Frequently occurring constraints are: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103604.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103605.png" /> is a function; <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103606.png" /> (where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103607.png" /> is the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103608.png" />th component of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c1103609.png" />), an integrality constraint; or <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c110/c110360/c11036010.png" />, a binary constraint.

See also [[Linear programming|Linear programming]]; [[Mathematical programming|Mathematical programming]]; [[Discrete programming|Discrete programming]]; [[Integer programming|Integer programming]].