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Simplex algorithm
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==Other algorithms== Other algorithms for solving linear-programming problems are described in the [[linear programming|linear-programming]] article. Another basis-exchange pivoting algorithm is the [[criss-cross algorithm]].<ref>{{cite journal|last1=Terlaky|first1=Tamás|last2=Zhang|first2=Shu Zhong|title=Pivot rules for linear programming: A Survey on recent theoretical developments|issue=1|journal=Annals of Operations Research|volume=46–47|year=1993|pages=203–233|doi=10.1007/BF02096264|mr=1260019|citeseerx = 10.1.1.36.7658 |s2cid=6058077|issn=0254-5330}}</ref><ref>{{cite journal|first1=Komei|last1=Fukuda|author1-link=Komei Fukuda|first2=Tamás|last2=Terlaky|author2-link=Tamás Terlaky|title=Criss-cross methods: A fresh view on pivot algorithms |journal=Mathematical Programming, Series B|volume=79|number=1–3|pages=369–395|editor1=Thomas M. Liebling |editor2=Dominique de Werra|publisher=North-Holland Publishing |location=Amsterdam|year=1997|doi=10.1007/BF02614325|mr=1464775|s2cid=2794181 |url=http://infoscience.epfl.ch/record/77270 }}</ref> There are polynomial-time algorithms for linear programming that use interior point methods: these include [[Khachiyan]]'s [[ellipsoidal algorithm]], [[Karmarkar]]'s [[Karmarkar's algorithm|projective algorithm]], and [[interior point method|path-following algorithm]]s.<ref name="Vanderbei"/> The [[Big_M_method|Big-M method]] is an alternative strategy for solving a linear program, using a single-phase simplex.
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