Cut Metamorphoses

Watching a run of the cutting-plane method is like viewing a tug-of-war between the LP solver and the cut finder. When a cutting plane is added to the LP relaxation, the solver often reacts by shifting the defect inx ∗prohibited by the cut to an area just beyond the cut’s control. This may be one explanation for the footnote in the Dantzig et al. [150] technical report remarking that E. W. Paxson called their procedure the “finger in the dike” method. One way to deal with the shifting LP solution is to respond to each slight adjustment ofx ∗