Convergence behavior of Karmarkar's projective algorithm for solving a simple linear program

Authors:
John A. Kaliski;Yinyu Ye
Affiliations:
Department of Management Sciences, The University of Iowa, Iowa City, IA 52242, USA;Department of Management Sciences, The University of Iowa, Iowa City, IA 52242, USA
Venue:
Operations Research Letters
Year:
1991

Citing 3
Cited 0

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Abstract

We describe the convergence behavior of Karmarkar's projective algorithm for solving a simple linear program. We show that the algorithm requires at least n - 1 iterations to reach the optimal solution, while the simplex method may need one pivot step. Thus in the worst case, Karmarkar's algorithm will require at least @W(n) iterations to converge.