A Note on Coefficient Adjustment Using Sos Constraints

Lougee-Heimer, Robin

doi:10.1287/opre.49.1.175.11184

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Multi-coefficient Adjustment1

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2005

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Cited by 2 publications

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“…Hoffman and Padberg (1991) essentially study this same system with the additional requirement that α ≥ 0, and propose an alternate strengthening method. A clarification of the first article and a generalization of the techniques in both papers is given in Lougee-Heimer (2001). These results directly derive from our conditional logic arguments in the following manner.…”

Section: Multi-coefficient Adjustmentmentioning

confidence: 65%

A Conditional Logic Approach for Strengthening Mixed 0-1 Linear Programs

Lougee-Heimer

Adams

2005

Ann Oper Res

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We study a conditional logic approach for tightening the continuous relaxation of a mixed 0-1 linear program. The procedure first constructs quadratic inequalities by computing pairwise products of constraints, and then surrogates modified such inequalities to produce valid linear restrictions. Strength is achieved by adjusting the coefficients on the quadratic restrictions. The approach is a unifying framework for published coefficient adjustment methods, and generalizes the process of sequential lifting. We give illustrative examples and discuss various extensions, including the use of more complex conditional logic constructs that compute and surrogate polynomial expressions, and the application to general integer programs.

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Section: Multi-coefficient Adjustmentmentioning

confidence: 65%