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The Klee–Minty cube is a perturbation of the cube shown here. |
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{{about|an [[algorithm]] for [[optimization (mathematics)|mathematical optimization]]|the naming of [[analytical chemistry|chemicals]]|crisscross method}}
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[[Image :Unitcube.svg|thumb|right|alt=A three-dimensional cube|The criss-cross algorithm visits all 8 corners of the [[Klee–Minty cube]] in the worst case. It visits 3 additional corners on average. The Klee–Minty cube is a perturbation of the cube shown here.]]
In [[optimization (mathematics)|mathematical optimization]], the '''criss-cross algorithm''' denotes a family of [[algorithm]]s for [[linear programming]]. Variants of the criss-cross algorithm also solve more general problems with [[linear programming|linear inequality constraints]] and [[nonlinear programming|nonlinear]] [[optimization (mathematics)|objective functions]]; there are criss-cross algorithms for [[linear-fractional programming]] problems,<ref name="LF99Hyperbolic">{{harvtxt|Illés|Szirmai|Terlaky|1999}}</ref> [[quadratic programming|quadratic-programming]] problems, and [[linear complementarity problem]]s.<ref name="FukudaTerlaky" > {{harvtxt|Fukuda|Terlaky|1997}} </ref>
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