On the Relationship of Interior-Point Methods

Ruey Lin Sheu, Shu Cherng Fang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)565-572
Number of pages8
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume16
Issue number3
DOIs
Publication statusPublished - 1993

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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