, Volume 44, Issue 1-3, pp 27-41

Interior path following primal-dual algorithms. part I: Linear programming

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Abstract

We describe a primal-dual interior point algorithm for linear programming problems which requires a total of \(O\left( {\sqrt n L} \right)\) number of iterations, whereL 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.