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Interior path following primaldual algorithms. part I: Linear programming
 Renato D. C. Monteiro,
 Ilan Adler
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We describe a primaldual 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 KarushKuhnTucker 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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 Title
 Interior path following primaldual algorithms. part I: Linear programming
 Journal

Mathematical Programming
Volume 44, Issue 13 , pp 2741
 Cover Date
 19890501
 DOI
 10.1007/BF01587075
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Interiorpoint methods
 linear programming
 Karmarkar's algorithm
 polynomialtime algorithms
 logarithmic barrier function
 path following
 Industry Sectors
 Authors

 Renato D. C. Monteiro ^{(1)}
 Ilan Adler ^{(1)}
 Author Affiliations

 1. Department of Industrial Engineering and Operations Research, University of California, 94720, Berkeley, CA, USA