On the relationship of interior-point methods

Ruey-Lin Sheu and Shu-Cherng Fang

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-8

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:595972

DOI: 10.1155/S0161171293000699

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