Abstract
We describe an extension of Karmarkar's algorithm for linear programming that handles problems with unknown optimal value and generates primal and dual solutions with objective values converging to the common optimal primal and dual value. We also describe an implementation for the dense case and show how extreme point solutions can be obtained naturally, with little extra computation.
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Communicated by Nimrod Megiddo.
Research supported in part by a fellowship from the Alfred P. Sloan Foundation and by NSF Grant ECS-15361.
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Todd, M.J., Burrell, B.P. An extension of Karmarkar's algorithm for linear programming using dual variables. Algorithmica 1, 409–424 (1986). https://doi.org/10.1007/BF01840455
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DOI: https://doi.org/10.1007/BF01840455