Abstract
The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration. We present a variant of the Karmarkar algorithm that uses standard variable-metric techniques in an innovative way to approximate this projection. In limited tests, this modification greatly reduces the number of matrix factorizations needed for the solution of linear programming problems.
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Research sponsored by DOE DE-AS05-82ER13016, ARO DAAG-29-83-K-0035, AFOSR 85-0243.
Research sponsored by ARO DAAG-29-83-K-0035, AFOSR 85-0243, Shell Development Company.
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Dennis, J.E., Morshedi, A.M. & Turner, K. A variable-metric variant of the Karmarkar algorithm for linear programming. Mathematical Programming 39, 1–20 (1987). https://doi.org/10.1007/BF02592068
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DOI: https://doi.org/10.1007/BF02592068