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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.
 Bayer, D.A., Lagarias, J.C. (1986) The nonlinear geometry of linear programming. AT&T Bell Laboratories, Murray Hill, NJ
 Fiacco, A., McCormick, G. (1968) Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley and Sons, New York
 Frisch, K.R. (1955) The logarithmic potential method of convex programming. University Institute of Economics, Oslo, Norway
 Gill, P.E., Murray, W., Saunders, M.A., Tomlin, J.A., Wright, M.H. (1986) On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method. Mathematical Programming 36: pp. 183209
 Gonzaga, C.C. (1987) “An algorithm for solving linear programming problems in O(n 3 L) operations,” Memorandum Number UCB/ERL M87/10. Electronics Research Laboratory, Universtiy of California, Berkeley, CA
 Karmarkar, N. (1984) A new polynomial time algorithm for linear programming. Combinatorica 4: pp. 373395
 N. Karmarkar, Talk at the University of California at Berkeley (Berkeley, CA, 1984).
 Kojima, M., Mizuno, S., Yoshise, A. (1987) “A primaldual interior point algorithm for linear programming,” Report No. B188. Department of Information Sciences, Tokyo Institute of Technology, Tokyo, Japan, February
 Megiddo, N. (1986) “Pathways to the optimal set in linear programming,” Research Report. IBM Almaden Research Center, San Jose, CA
 Papadimitriou, C.R., Steiglitz, K. (1982) Combinatorial Optimization: Algorithms and Complexity. PrenticeHall, Englewood Cliffs, New Jersey
 Renegar, J. (1988) A polynomialtime algorithm based on Newton's method for linear programming. Mathematical Programming 40: pp. 5993
 Vaidya, P.M. (1987) An algorithm for linear programming which requires O(((m + n)n 2+(m + n) 1.5 n)L) arithmetic operations. AT&T Bell Laboratories, Murray Hill, NJ
 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