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* '''Potential reduction methods''': [[Karmarkar algorithm|Karmarkar's algorithm]] was the first one.
* '''Path-following methods''': the algorithms of [[James Renegar]]<ref name=":1">{{Cite journal |last=Renegar |first=James |date=1988-01-01 |title=A polynomial-time algorithm, based on Newton's method, for linear programming |url=https://doi.org/10.1007/BF01580724 |journal=Mathematical Programming |language=en |volume=40 |issue=1 |pages=59–93 |doi=10.1007/BF01580724 |issn=1436-4646|url-access=subscription }}</ref> and Clovis Gonzaga<ref name=":2">{{Citation |last=Gonzaga |first=Clovis C. |title=An Algorithm for Solving Linear Programming Problems in O(n3L) Operations |date=1989 |url=https://doi.org/10.1007/978-1-4613-9617-8_1 |work=Progress in Mathematical Programming: Interior-Point and Related Methods |pages=1–28 |editor-last=Megiddo |editor-first=Nimrod |access-date=2023-11-22 |place=New York, NY |publisher=Springer |language=en |doi=10.1007/978-1-4613-9617-8_1 |isbn=978-1-4613-9617-8|url-access=subscription }}</ref> were the first ones.
* '''Primal-dual methods'''.
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