An interior point method, based on rank-1 updates, for linear programming

Jos F. Sturm, Shuzhong Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We propose a polynomial time primal-dual potential reduction algorithm for linear programming. The algorithm generates sequences dk and vk rather than a primal-dual interior point (xk,sk), where dki = √xki/ski and vki = √xkiski for i = 1, 2, . . . , n. Only one element of dk is changed in each iteration, so that the work per iteration is bounded by O(mn) using rank-1 updating techniques. The usual primal-dual iterates xk and sk are not needed explicitly in the algorithm, whereas dk and vk are iterated so that the interior primal-dual solutions can always be recovered by aforementioned relations between (xk,sk) and (dk,vk) with improving primal-dual potential function values. Moreover, no approximation of dk is needed in the computation of projection directions.

Original languageEnglish (US)
Pages (from-to)77-87
Number of pages11
JournalMathematical Programming, Series B
Issue number1
StatePublished - Mar 1 1998
Externally publishedYes


  • Interior point method
  • Linear programming
  • Potential function


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