International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 565-572
doi:10.1155/S0161171293000699
On the relationship of interior-point methods
Ruey-Lin Sheu1
and Shu-Cherng Fang2
1AT\&T Bell Laboratories, Holmdel, USA
2Operations Research \& Industrial Engineering, North Carolina State University, Box 7913, Raleigh 27695-7913, NC, USA
Abstract
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.