On the relationship of interior-point methods
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 pa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000699 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |