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.
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Monteiro, R.D.C., Adler, I. Interior path following primal-dual algorithms. part I: Linear programming. Mathematical Programming 44, 27–41 (1989). https://doi.org/10.1007/BF01587075
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DOI: https://doi.org/10.1007/BF01587075