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2010

Relations between facets of low- and high-dimensional group problems

10 years 2 months ago
Relations between facets of low- and high-dimensional group problems
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...
Santanu S. Dey, Jean-Philippe P. Richard
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where MP
Authors Santanu S. Dey, Jean-Philippe P. Richard
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