Simplex algorithm: Difference between revisions

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The name of the algorithm is derived from the concept of a [[simplex]] and was suggested by [[Theodore Motzkin|T. S. Motzkin]].<ref name="Murty22" >{{harvtxt|Murty|1983|loc=Comment 2.2}}</ref> Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial ''[[cone (geometry)|cone]]s'', and these become proper simplices with an additional constraint.<ref name="Murty39">{{harvtxt|Murty|1983|loc=Note 3.9}}</ref><ref name="StoneTovey">{{cite journal|last1=Stone|first1=Richard E.|last2=Tovey|first2=Craig A.|title=The simplex and projective scaling algorithms as iteratively reweighted least squares methods|journal=SIAM Review|volume=33|year=1991|issue=2|pages=220–237
|mr=1124362|jstor=2031142|doi=10.1137/1033049}}</ref><ref>{{cite journal|last1=Stone|first1=Richard E.|last2=Tovey|first2=Craig A.|title=Erratum: The simplex and projective scaling algorithms as iteratively reweighted least squares methods|journal=SIAM Review|volume=33|year=1991|issue=3|pages=461|mr=1124362|doi=10.1137/1033100|jstor=2031443|ref=harv}}</ref><ref name="Strang">{{cite journal|last=Strang|first=Gilbert|authorlink=Gilbert Strang|title=Karmarkar's algorithm and its place in applied mathematics|journal=[[The Mathematical Intelligencer]]|year=1987|month=1 June|
publisher=Springer|___location=New York|issn=0343-6993|pages=4–10|volume=9|doi=10.1007/BF03025891|mr='''883185'''|ref=harv|issue=2}}</ref> The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a [[polytope]]. The shape of this polytope is defined by the [[System of linear inequalities|constraints]] applied to the objective functionfunctions.
 
== Overview ==