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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| _version_ | 1832558489704071168 |
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| author | Ruey-Lin Sheu Shu-Cherng Fang |
| author_facet | Ruey-Lin Sheu Shu-Cherng Fang |
| author_sort | Ruey-Lin Sheu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ee2fbebbcb3d45dcad32124142a770b6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ee2fbebbcb3d45dcad32124142a770b62025-02-03T01:32:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116356557210.1155/S0161171293000699On the relationship of interior-point methodsRuey-Lin Sheu0Shu-Cherng Fang1AT&T Bell Laboratories, Holmdel, USAOperations Research & Industrial Engineering, North Carolina State University, Box 7913, Raleigh, NC 27695-7913, USAIn 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.http://dx.doi.org/10.1155/S0161171293000699linear programminginterior-point methodNewton method duality theory. |
| spellingShingle | Ruey-Lin Sheu Shu-Cherng Fang On the relationship of interior-point methods International Journal of Mathematics and Mathematical Sciences linear programming interior-point method Newton method duality theory. |
| title | On the relationship of interior-point methods |
| title_full | On the relationship of interior-point methods |
| title_fullStr | On the relationship of interior-point methods |
| title_full_unstemmed | On the relationship of interior-point methods |
| title_short | On the relationship of interior-point methods |
| title_sort | on the relationship of interior point methods |
| topic | linear programming interior-point method Newton method duality theory. |
| url | http://dx.doi.org/10.1155/S0161171293000699 |
| work_keys_str_mv | AT rueylinsheu ontherelationshipofinteriorpointmethods AT shucherngfang ontherelationshipofinteriorpointmethods |