A complete constructive algorithm for the general mixed linear programming problem

Glenn W. Graves

Naval Research Logistics Quarterly, 1965, vol. 12, issue 1, 1-34

Abstract: An algorithm that seems to have several advantages for application to the general mixed linear programming problem is described. Although it does not make any non‐degeneracy assumption or stipulate conditions for consistency of constraints or finiteness of extrenal value, it has the following distinct advantages: (1) it does away with all augmentation for any reason, in particular “artificial variables” for “initial feasible solutions” and the doubling of rows and columns for equations and variables of arbitrary sign; (2) it does not resort to any perturbation technique or arbitrary cycling of “basis” to cope with the “degeneracy problem,” but instead shows how to capitalize on it by concentrating on a greatly restricted subset of rows and columns; (3) it isolates and identifies inconsistent constraints in a simple, natural way; and (4) it features a small segregated inverse of a “basic kernel,” opening the way to easy generation of elements techniques with large sparse systems.

Date: 1965
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https://doi.org/10.1002/nav.3800120102

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