Some Relations Between Facets of Low- and High-Dimensional Group Problems
نویسندگان
چکیده
In this paper, we introduce an operation that creates families of facet-defining inequalities for highdimensional infinite group problems using facet-defining inequalities of lower-dimensional group problems. We call this family sequential-merge inequalities because they are produced by applying two group cuts one after the other and because the resultant inequality depends on the order of the operation. The sequentialmerge inequalities can be used to generate inequalities whose continuous variables coefficients are stronger than those of the constituent low-dimensional cuts. We also show that they can be used to derive the three-gradient facet-defining inequality introduced by Dey and Richard. We then introduce a general scheme for generating valid inequalities for lower-dimensional group problems using valid inequalities of higher-dimensional group problems. We present conditions under which this construction generates facetdefining inequalities when applied to sequential-merge inequalities. We show that this procedure generates a subfamily of the two-step MIR inequalities of Dash and Günlük.
منابع مشابه
Relations between facets of low- and high-dimensional group problems
One-dimensional infinite group problems have been extensively studied and have yielded strong cutting planes for mixed integer programs. Although numerical and theoretical studies suggest that group cuts can be significantly improved by considering higher-dimensional groups, there are no known facets for infinite group problems whose dimension is larger than two. In this paper, we introduce an ...
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