文章基本信息

标题：On the relationship of interior-point methods
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作者：Ruey-Lin Sheu ; Shu-Cherng Fang
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1993
卷号：16
DOI：10.1155/S0161171293000699
出版社：Hindawi Publishing Corporation
摘要：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.