A modified lift-and-project procedure

A modified lift-and-project procedure

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Article ID: iaor1999894
Country: Netherlands
Volume: 79
Issue: 1/3
Start Page Number: 19
End Page Number: 31
Publication Date: Oct 1997
Journal: Mathematical Programming
Authors:
Keywords: programming: integer
Abstract:

In recent years the lift-and-project approach has been used successfully within a branch-and-cut framework to solve large, difficult pure and mixed 0–1 programs that have resisted solution efforts by pure branch and bound codes. The approach uses a linear description in a higher dimensional space of the convex hull of the disjunctive set created by imposing one or several 0–1 conditions. By solving a linear program derived from this higher dimensional representation – the cut generating linear program (CGLP) – the standard lift-and-project procedure obtains a deepest cut in a well defined sense. We propose a modification of CGLP that allows us to generate not just one deepest cut, but a class of cuts with desirable properties, each at the cost of one extra pivot in the optimal tableau of the modified CGLP.

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