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International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 565-572

On the relationship of interior-point methods

1AT&T Bell Laboratories, Holmdel, USA
2Operations Research & Industrial Engineering, North Carolina State University, Box 7913, Raleigh, NC 27695-7913, USA

Received 20 February 1992; Revised 13 October 1992

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic “paths” that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. We also derive the missing dual information in the primal-affine scaling method and the missing primal information in the dual-affine scaling method. Basically, the missing information has the same form as the solutions generated by the primal-dual method but with different scaling matrices.