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Interior path following primal-dual algorithms. I: Linear programming. (English) Zbl 0676.90038

Authors’ abstract: “We describe a primal-dual interior point algorithm for linear programming problems which requires a total of O(nL) 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).]

Reviewer: N.Deng

MSC:
90C05Linear programming
65K05Mathematical programming (numerical methods)
68Q25Analysis of algorithms and problem complexity
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