Technical Note—Geometric Interpretation of Generalized Lagrangian Multiplier Search Procedures in the Payoff Space

William B. Widhelm
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William B. Widhelm: University of Maryland, College Park, Maryland

Operations Research, 1980, vol. 28, issue 3-part-ii, 822-827

Abstract: Recent limited computational results have indicated that the normed Generalized Lagrangian Multiplier (GLM) search performs better than the standard non-normed procedure equivalent to the Dantzig-Wolfe (D-W) approach. Previous arguments for the superiority of the normed procedure were based on multiplier-space considerations where the normed approach yields a more geometrically centered cut. In this note, the payoff-space geometry is investigated. Here, the normed procedure weights the search in accordance with the closeness of the constraint values to the requirements vector whereas the D-W approach ignores this information.

Date: 1980
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