Simplex algorithm: Difference between revisions

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{{about|the linear programming algorithm|the non-linear optimization heuristic|Nelder–Mead method}}

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In [[optimization (mathematics)|mathematical optimization]], [[George Dantzig|Dantzig]]'s '''simplex algorithm''' (or '''simplex method''') is a popular, (but widely hated by students) [[algorithm]] for [[linear programming]].<ref name="Murty">{{cite book|last=Murty|first=Katta G.|author-link=Katta G. Murty|title=Linear programming|publisher=John Wiley & Sons Inc.1, 2000 |url=http://www.computer.org/csdl/mags/cs/2000/01/c1022.html}}</ref>

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