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Determining basic variables of optimal solutions in Karmarkar's new LP algorithm

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Abstract

This paper establishes a sufficient condition for a variable of a linear program to be positive at all optimal solutions. A numerical test using the condition is incorporated into Karmarkar's new LP algorithm to determine columns of optimal basis. Experimental results on the test are also reported.

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Communicated by Nimrod Megiddo.

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Kojima, M. Determining basic variables of optimal solutions in Karmarkar's new LP algorithm. Algorithmica 1, 499–515 (1986). https://doi.org/10.1007/BF01840459

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  • DOI: https://doi.org/10.1007/BF01840459

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