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 27695-7913, NC, USA
Received 20 February 1992; Revised 13 October 1992
Copyright © 1993 Ruey-Lin Sheu and Shu-Cherng Fang. 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.