Improved Bounds for Integer Programs: A Supergroup Approach

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/40 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/40 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/40 archive 351 disk0/00/00/00/57 2016-01-15 01:40:37 2021-08-27 17:07:21 2016-01-15 01:40:37 monograph show 2 Bell D.E. AL0482 Improved Bounds for Integer Programs: A Supergroup Approach pub iis_met prog_sds Recent work by Fisher and Shapiro has used Gomory's group theoretic methods together with Lagrange multipliers to obtain bounds for the optimal value of integer programs. Here it is shown how an extension of the associated abelian group to a supergroup can improve the bound without the artificiality of adding a cut. It is proved that there exists a finite group for which the dual ascent procedure of Fisher and Shapiro converges to the optimal integer solution. Constructive methods are given for finding this group. A worked example is included. 1973-11 published RM-73-005 RM-73-005 10 1722 public research_memorandum IIASA, Laxenburg, Austria 17 FALSE info:eu-repo/semantics/book