Abstract
In this note, we first observe that the Morshedi-Tapia interpretation of the Karmarkar algorithm naturally offers an extension of the Karmarkar subproblem scaling to problems with free variables. We then note that this extended scaling is precisely the scaling suggested by Mitchell and Todd for problems with free variables. Mitchell and Todd gave no motivation for or justification of this extended scaling.
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References
Morshedi, A. M., andTapia, R. A.,Karmarkar as a Classical Method, Mathematical Sciences Technical Report No. 87-7, Rice University, 1987.
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Mitchell, J. E., andTodd, M.,A Variant of Karmarkar's Linear Programming Algorithm for Problems with Some Unrestricted Variables, SIAM Journal on Matrix Analysis and Applications, Vol. 10, pp. 30–38, 1989.
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Communicated by R. A. Tapia
This research was sponsored by NSF Cooperative Agreement No. CCR-88-09615, AFOSR Grant 89-0363, DOE Grant DEFG05-86-ER25017, ARO Grant 9DAAL03-90-G-0093, and COLCIENCIAS CO: 1106-05-307-93.
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Martínez, H.J. On motivating the Mitchell-Todd modification of Karmarkar's algorithm for LP problems with free variables. J Optim Theory Appl 84, 675–679 (1995). https://doi.org/10.1007/BF02191992
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DOI: https://doi.org/10.1007/BF02191992