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Zbl 0676.90038
Monteiro, Renato D.C.; Adler, Ilan
Interior path following primal-dual algorithms. I: Linear programming.
(English)
[J] Math. Program., Ser. A 44, No.1, 27-41 (1989). ISSN 0025-5610; ISSN 1436-4646/e

Authors' abstract: We describe a primal-dual interior point algorithm for linear programming problems which requires a total of O($\sqrt{n}L)$ number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.'' \par [For part II see the authors, ibid. A 44, No.1, 43-66 (1989; Zbl 0676.90039).]
[N.Deng]
MSC 2000:
*90C05 Linear programming
65K05 Mathematical programming (numerical methods)
68Q25 Analysis of algorithms and problem complexity

Keywords: polynomial-time algorithms; primal-dual interior point algorithm; logarithmic barrier function; path following

Citations: Zbl 0676.90039

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