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

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.