an:04108479
Zbl 0676.90038
Monteiro, Renato D. C.; Adler, Ilan
Interior path following primal-dual algorithms. I: Linear programming
EN
Math. Program., Ser. A 44, No. 1, 27-41 (1989).
00155088
1989
j
90C05 65K05 68Q25
polynomial-time algorithms; primal-dual interior point algorithm; logarithmic barrier function; path following
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.''
[For part II see the authors, ibid. A 44, No.1, 43-66 (1989; Zbl 0676.90039).]
N.Deng
Zbl 0676.90039