1. What have the authors contributed in "On mixed-integer sets with two integer variables" ?
The authors show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut ( which they defined recently in [ 3 ] ).. The authors then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables provided that the coefficients of the integer variables form a matrix of rank 2.. The authors also present an alternative characterization of the crooked cross cut closure of mixed-integer sets similar to the one about the equivalence of different definitions of split cuts presented in Cook, Kannan, and Schrijver [ 4 ].
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